vxEPA
United States
Environmental Protection
Agency
EPA Unmix 6.0 Fundamentals
& User Guide
RESEARCH AND DEVELOPMENT
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EPA/600/R-07/089
June 2007
vwwv.epa.gov
EPA Unmix 6.0 Fundamentals
& User Guide
Gary Morris, Ram Vedantham, Rachelle Duvall
U.S. Environmental Protection Agency
National Exposure Research Laboratory
Research Triangle Park, NC 27711
Ronald C. Henry
24017 Ingomar Street
West Hills, CA 91304
U.S. Environmental Protection Agency
Office of Research and Development
Washington, DC 20460
Notice: Although this work was reviewed by EPA and approved for publication, it may not necessarily reflect official
Agency policy. Mention of trade names and commercial products does not constitute endorsement or
recommendation for use.
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Disclaimer
EPA through its Office of Research and Development funded and managed the
research and development described here. The User Guide has been subjected
to Agency review and is cleared for official distribution by the EPA. Mention of
trade names or commercial products does not constitute endorsement or
recommendation for use.
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EPA Unmix 6.0 Fundamentals & User Guide
TABLE OF CONTENTS
Disclaimer
TABLE OF CONTENTS.
LIST OF FIGURES
LIST OF TABLES iv
SECTION 1. INTRODUCTION 1
SECTION 2. INSTALLING Unmix 2
2.1 Hardware and Software Requirements 2
2.2 Installation Directions 2
2.3 Testing the Installation 2
SECTION 3. BASIC OPERATIONS 3
3.1 Input Data 4
3.2 Suggest Exclusion 6
3.3 Initial Species 10
3.4 Suggest Additional Species 13
3.5 Plot Distribution 17
3.6 Evaluating Results 17
3.7 No Feasible Solution 22
3.8 Estimate Source Profile Uncertainties 23
3.9 Run Profiles 30
SECTION 4. AUTO Unmix 32
SECTION 5. ADVANCED OPERATIONS 37
5.1 Influential Observations 38
5.2 Influential Points 43
5.3 Apportionment of Species Not in the Model 49
5.4 Factor Analysis 52
5.5 Replace Missing Data 54
SECTION 6. ADVANCE PLOTTING OPTIONS 59
6.1 Figure Groups 60
6.2 Edge Plots 62
SECTION 7. BATCH MODE 67
SECTION 8. Unmix PUBLICATIONS 72
APPENDIX A: INSTRUCTIONS FOR RUNNING UNDER WINDOWS VISTA _74
APPENDIX B: INSTALLING A NEW VERSION OF EPA Unmix 75
APPENDIX C: VARIABILITY CALCULATION ALGORITHM 76
APPENDIX D: PROCEDURE DIAGRAMS 85
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EPA Unmix 6.0 Fundamentals & User Guide
LIST OF FIGURES
Figure 1: Main window 3
Figure 2: Input Data File 5
FigureS: Data Processing window 6
Figure 4: Suggest Exclusion 8
Figure 5: Included and Excluded Species 9
Figure 6: Select Initial Species 11
Figure 7: Initial Species Source Profiles 12
Figure 8: Initial Selected Species 13
Figure 9: Suggest Additional Species 14
Figure 10: Suggestion Species 15
Figure 11: Suggest Additional Species Source Profiles 16
Figure 12: Analysis Results - Plot Distribution 17
Figure 13: Analyze Output window 18
Figure 14: Analysis Results- Fit Diagnostics Example 19
Figure 15: Diagnostic Plots - Fit Diagnostics Example 21
Figure 16: Partial Solution 23
Figure 17: Variability Estimate Plot 26
Figure 18: Source Profile Variability Plot 27
Figure 19: Species Report (percentile based) 29
Figure 20: Save Current Run Choices 31
Figure 21: Umx File 32
Figure 22: Auto Unmix command 35
Figure 23: AU result for wdcpmdata 36
Figure 24: AU Source Profiles 37
Figure 25: View/Edit Observations & Points 39
Figure 26: View/Edit Observations & Points plot high OC1 point 40
Figure 27: New edges in View/Edit Observations & Points plot 41
Figure 28: Data Processing Report 42
Figure 29: Datacursor Mode 43
Figure 30: Example STN PM data set 45
Figure 31: Example STN PM excluded species 46
Figure 32: Influential Points command 47
Figure 33: Influential potassium point 48
Figure 34: Influential points 49
Figure 35: Fit Unselected Species command 50
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EPA Unmix 6.0 Fundamentals & User Guide
Figure 36: Fit Unselected Species Results 51
Figure 37: Adding species from Fit Unselected Species 52
Figure 38: Factor Analyze Selections command 53
Figure 39: Factor Analysis Results 54
Figure 40: Replace Missing Values command 57
Figure 41: Replaced missing values 58
Figure 42: Comparison of umtestR and umtest results 59
Figure 43: Saving Diagnostic Plots 60
Figure 44: Source profile plots 61
Figure 45: Figure groups 62
Figure 46: Umpdata edge plot example 63
Figure 47: Umpdata source profiles 64
Figure 48: Edge Plots 65
Figure 49: Selected Points in Edge Plots 66
Figure 50: Example of poorly defined edges 67
Figure 51: Batch mode influential point option 68
Figure 52: Batch Mode Preferences 69
Figure 53: Batch Mode Solution Summary 70
Figure 54: Batch Mode Analysis Results 71
LIST OF TABLES
Table 1: Input Data Parameters 4
Table 2: Fit Diagnostics Guidance 20
Table 3: Missing Value Estimation 56
IV
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EPA Unmix 6.0 Fundamentals & User Guide
SECTION 1. INTRODUCTION
The underlying philosophy of Unmix is to let the data speak for itself. Unmix
seeks to solve the general mixture problem where the data are assumed to be a
linear combination of an unknown number of sources of unknown composition,
which contribute an unknown amount to each sample. Unmix also assumes that
the compositions and contributions of the sources are all positive. Unmix
assumes that for each source there are some samples that contain little or no
contribution from that source. Using concentration data for a given selection of
species, Unmix estimates the number of sources, source compositions, and
source contributions to each sample.
It is well known that the general mixture problem and the special case of
multivariate receptor modeling are ill posed problems. There are simply more
unknowns than equations and thus there may be many wildly different solutions
that are all equally good in a least-squares sense. Statisticians say that these
problems are not identifiable. One approach to ill-posed problems is to impose
conditions that add additional equations, which then define a unique solution.
The most likely candidates for these additional conditions, or constraints, are the
non-negativity conditions imposed by the physical nature of the problem. Source
compositions and contributions must be non-negative. Unfortunately, it has been
shown that non-negativity conditions alone are not sufficient to give a unique
solution and more constraints are needed (Henry, 1987). Under certain rather
mild conditions, the data themselves can provide the needed constraints (Henry,
1997). This is how Unmix works. However, sometimes the data do not support a
solution. In this case Unmix will not find one. While some might judge this a
disadvantage, it is actually a positive benefit to the user. Few modeling
approaches let the user know clearly when a reliable solution is not possible.
If the data consists of many observations of M species, then the data can be
plotted in an M-dimensional data space where the coordinates of a data point are
the observed concentrations of the species during a sampling period. If there are
N sources, the data space can be reduced to an N-1-dimensional space. It is
assumed that for each source there are some data points where the contribution
of the source is not present or small compared to the other sources. These are
called edge points and Unmix works by finding these points and fitting a
hyperplane through them; this hyperplane is called an edge (if N = 3, the
hyperplane is a line). By definition, each edge defines the points where a single
source is not contributing. If there are N sources, then the intersection of N-1 of
these hyperplanes defines a point that has only one source contributing. Thus,
this point gives the source composition. In this way the composition of the N
sources are found, and from this the source contributions are calculated so as to
give a best fit to the data. The Unmix modeling process is explained by simple
graphical examples in Henry (1997), and a list of manuscripts that provide details
on the algorithms used by Unmix can be found in Section 8.
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EPA Unmix 6.0 Fundamentals & User Guide
The term "Source" should be considered short for "Source type." This more
general term accounts for the potential that there could be a cluster of sources
within short distances of each other and/or there could be multiple sources along
the wind flow pattern reaching the receptor thereby creating source types.
SECTION 2. INSTALLING Unmix
EPA Unmix 6.0 runs in a Microsoft Windows environment (2000, XP, and Vista).
Special instructions for running Unmix under the Windows Vista Operating
System are listed in Appendix A. When correctly installed, double clicking on the
icon (shown below) on the Desktop will start the program.
a,
EPA Unmix 6.0
2.1 Hardware and Software Requirements
The speed of execution depends on the memory, processor speed etc. of the
user's computer. A minimum of 80 Mb of disk space is required to install the
program.
2.2 Installation Directions
1) Download the installation executable from the File Transfer Protocol (FTP)
site.
2) Double-click on the EPA Unmix 6.0 Standalone lnstallation.exe file.
3) Follow the on-screen instructions to complete the installation.
If Unmix 6.0 has already been installed on your computer and you are updating the
program with a new version, please follow the instructions in Appendix B. To uninstall
Unmix, use the "Add or Remove Programs" option (from Start => Control Panel), select
the EPA Unmix 6.0 on the window that opens and press "Remove. " After that, also
remove Matlab Component Runtime (MCR) program from the same list. Please be aware
that this process does not completely remove all files related to EPA Unmix 6.0. Files
and folders that may have been created on your computer cannot be removed by this
process. Those will have to be removed individually.
2.3 Testing the Installation
Double click the EPA Unmix 6.0 icon. The first time the program is run, MATLAB
creates a machine copy of the code in the MCR folder. This slightly increases
the amount of time to start the program and subsequent use of the model will not
require re-creation of the code.
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EPA Unmix 6.0 Fundamentals & User Guide
An EPA disclaimer will first be displayed. Select OK and the program's Main
Window Graphic User Interface (GUI) will be displayed.
File Select Analyze Selected Species Tools Help
^^^m
Selected Species
Run #$ Species #0bs f Sources Min. Mm. Run
Rsq SigjNoise Type
Analyze Run I Highlight Run Output I Diagnostic Plots
Figure 1: Main window
It should be noted that a prolonged session of use of EPA Unmix can lead to
slower and slower response. This is due to the intensity of memory manipulation
required by a scientific program compared to a word processing program.
Memory allocations tend to become fragmented and memory management uses
more and more of the available computer resources. As such, the Windows
Operating System (OS) is not ideally suited for intense scientific computations.
When the program response speed appears to slow down perceptibly, the user
should save the current profile, shut down the program, and re-start the program.
SECTION 3. BASIC OPERATIONS
This section walks through the basic sequence of operations to produce a
receptor model of the data consisting of the source compositions and source
contributions that reproduce the data. Unmix procedure diagrams that cover
both the basic and advanced operations can be found in Appendix D.
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EPA Unmix 6.0 Fundamentals & User Guide
The following discussions assume that the program has been installed in the
default directory of C:\Program Files\EPA Unmix 6.0. Please make appropriate
changes if the program has been installed in a directory other than the one
mentioned above.
3.1 Input Data
Unmix accepts delimited (*.txt, *.dat, *.csv) and Microsoft Excel data files. Files
with dates and dates and time can also be used. The species names must be
placed in the first row of the data file and if dates (mm/dd/yyyy) or dates and
times (hh:mm) are provided they must be placed in the first and first and second
columns, respectively. Missing values can either be characters (e.g. XX) or
specific numerical values (e.g.-99).
The recommended units for input files are ppb for gases such as N02 and S02,
ppm for CO, and ng/m3 for PM mass and species. Replace negative or zero data
with half the method detection limit for the species. If zero values are in the data
set, a warning message will appear and the number of zero values for each
species will be displayed in the Data Processing window. Table 1 provides a
summary of the input data parameters.
Table 1: Input Data Parameters
Data File Types
Delimited *txt, *dat, *csv, or *xls
Data Location:
Species Names
Date Only
Date & Time
First row of data file
First column of data file
First and second columns of data file
Data Format:
Date
Time
Missing Values
MM/DD/YYYY (e.g. January 1, 2007 =
01/01/2007)
HH:MM in 24 hour cycle (e.g. 1:45 PM = 13:45)
Characters (e.g. XX) or Numerical Values (e.g.
-99)
Recommended Units:
N02 or S02
CO
PM Mass & Species
ppb
ppm
iig/m3
Negative or Zero Data
Replace with 1/2 the method detection limit for
the species
Five example data files have been provided that are located in the C:\Program
Files\EPA Unmix 6.0\Data folder. A data file is read by selecting the File ^ New
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EPA Unmix 6.0 Fundamentals & User Guide
Input Data command in the upper left corner of the main window. The input data
file window will open as shown in Figure 2. Input data file errors are typically
caused by not correctly identifying the file's date and time information on the
Input Data File window.
EPA Unmix 6.0
File Select Analyze Selected Species Tools Help
Figure 2: Input Data File
Input the file wdcpmdata.txt from the C:\Program Files\EPA Unmix 6.0\Data
folder. These data are from the Washington, D.C. Interagency Monitoring of
Protected Visual Environments (IMPROVE) PM monitoring site. Date information
is included in the file and the missing value symbol or code is -99. The Unmix
Data Processing window will open as shown in Figure 3 after inputting the data.
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EPA Unmix 6.0 Fundamentals & User Guide
Analysis Results • EPA Unmix 6.0
> Data Processing - EPA Unmix 6.0
File Specie? Paints and Observations About
Process Input Data
Input Filei
I Included Species
I Name
View/Edit Points and
Observations
Oo not replace or use highlighted species
Replace Missing Values
Data Processing Report
Excluded Species
Help
F
!2
3
1
2
3
4
IK
4
1173 16. ES3S
1195 0.0010
1199 0.0048
1199 0.0447
16 0.3SS3
1199 0.0040
1193 1.3422
1199 0.0022
1193 2.9563
1199 0.0064
6. 4463
0.0003
0.0019
0.0188
0.2429
0. 0013
0.5387
0. 0014
1.2372
0. 0036
3. 0725
0.0005
0.0027
0.0351
0.3061
0. 0030
0.801S
0.0022
1.7096
O.D071
Suggest Exclusion
Restore Original Data
Save Input Data
^"1™
Cancel OK
Figure 3: Data Processing window
A number of statistical parameters are displayed for each species: number of
observations (# obs), mean, average absolute deviation (AAD), and the standard
deviation (SD). The AAD is defined as themean(\Y -Y), where 7 is the species
concentration, Y is the mean of the species concentrations, and Y is the
absolute value of 7. This measure does not square the distance from the mean,
so it is less affected by extreme observations.
3.2 Suggest Exclusion
The results of all multivariate receptor models are degraded by including species
in the model that are dominated by noise. Inevitably, errors in the noisy species
will spread to all the sources determined by the model. Thus, it is best to remove
species that are known to have a high level of noise from possible inclusion in
the model. A general caveat concerning selection of species is in order.
Sometimes more is less, that is, adding more species to the model can, under
certain conditions, be detrimental to the model. Usually, the greater the number
of species, the model produces more accurate and stable results. The additional
information or 'signal' contributed by adding a species is larger than the error or
'noise'. However, if the species has a lot of error, it will to some degree mix into
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EPA Unmix 6.0 Fundamentals & User Guide
the whole model and corrupt the results. Thus, the model may have a better
signal-to-noise ratio without the species in question. Generally, it is best to first
add species that have the smallest measurement error.
Upon request, Unmix will provide a recommendation of species to exclude from
the analysis. To utilize this feature, select the Suggest Exclusion button located
in the data processing window and consider all species. You can use this tool on
a small set of species or all of the species. For a small set of species, highlight
the species you wish to include before pressing the "Suggest Exclusion" button.
Factor analysis is used to estimate the fraction of the variance of each species
associated with factors it has in common with other species and the fractional
amount that is associated uniquely with each species (technically known as the
uniqueness). It is recommended that species with more than 50 percent of the
variance due to error, or specific variance (SV) be considered for exclusion from
further Unmix modeling. However, if there is a species that is known to be
important and it has only a little more than 50 percent error, then it should not be
excluded from the modeling process. In addition, species that are suggested for
exclusion can be further evaluated using the View/Edit Points and Observations
(in particular the View Time Series Plots, View/Edit Observations and Points, and
View/Edit Influential Points commands) by selecting the appropriate option and
choosing the currently highlighted species option in the ensuing options window.
To unselect a species, hold the Ctrl key and click the left mouse key on the
species you wish to unselect.
It is best to first exclude all species that do not pass even the minimum quality
requirements. These excludable species may be those with a low number of
observations or species with a low number of concentrations above the detection
limit. For the wdcpmdata data, first select the species that you want to exclude
from Unmix analysis. Select (highlight) OMC (organic carbon x constant for
converting measured carbon to organic mass), ammS04, ammNOS, S02 (gas),
and OP (pyrolized carbon). Then, select the Exclude button to move the species
to the Excluded Species box.
The remaining species may be subject to more rigorous mathematical testing to
determine if they are compatible with the rest of the data set. Select the Suggest
Exclusion button and choose the "All Included" in the ensuing question box. After
a few moments, a message will be displayed stating that some of the species
have over 75% of their values missing. The species with the low number of
values are Cl and Zr which only have 16 and 192 values (MF or mass has 1178
values), respectively. Select OK and the species that are recommended for
exclusion will appear highlighted. Species such as NA are recommended for
exclusion because they have a SV greater than 0.50 or 50 percent. Select the
Exclude button to move the selected species from the Included to Excluded
Species box. The highlighted species are shown in Figure 4 and the lists of
included and excluded species are shown in Figure 5.
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EPA Unmix 6.0 Fundamentals & User Guide
I File Species Points and Observations About
Process Input Data
Input Filename:
| Included Species
cvrogram FuesiEPft Urort • b E
View/Edit Points and
Observations
Select One
192 0.0006
[3 Do not replace or use highlighted species
Replace Missing Values
Data Processing Report
16 Q.3ES3
1199 0.001E
1193 1.34Z2
1199 0.1301
0.2429 0.3061
0.0007 0.0009 0.57
0, 5387 0.8016 0. 00
0.0457 0.0615 0.61
:-ss i-ii?* s-i!
0. 0665 0. 1334 0. 00
|sos
imSQ4
• amrnHOS
IOHC
Help
Save Input Data
^••^
Cancel OK
Figure 4: Suggest Exclusion
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Data Processing - EPA Unmix 6.0
File Specie? Paints and Observations About
_J Do not replace or use highlighted species
Figure 5: Included and Excluded Species
The included species from this window will be displayed on the main Unmix
window after selecting the OK button. In the main Unmix window, species listed
in the Selected Species box are used in the Unmix analysis. Species can be
moved from the Unselected Species box to the Selected Species box by
highlighting the specie(s) in the Unselected Species box and selecting the <-
button. Species can also be moved to the Unselected Species box by
highlighting the specie(s) in Selected Species box and selecting the -> button. It
is important to differentiate between excluded species and unselected species.
The excluded species are simply not included in the analysis. Unselected
species are available. They are essentially on the sidelines and can be brought in
anytime for analysis.
The three buttons below the two arrow buttons are used to identify the species
highlighted in the left-hand side selection box as the total species (TS), a tracer
species (only emitted by one source), or the variable used to normalize the
source compositions. Usually the normalization and TS are the same, as this
gives a source composition as a mass fraction. However, in some applications,
one may wish to normalize to some standard species to be consistent with other
reported normalized compositions. In this case the normalization species will not
be the same as the TS. If a TS is set, Unmix tests the source compositions to
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EPA Unmix 6.0 Fundamentals & User Guide
ensure that the sum of the species in a source is not greater than the TS. Thus,
if the user wants Unmix to apply this constraint, Unmix must be informed as to
which species is the total species. The total, tracer and the norm species buttons
are toggle buttons. That is, after highlighting a species in the Selected Species
window (left side box), repeated pressing of these buttons will alternatively select
and unselect the chosen species as the requested type of species. Once a
species is selected as a total, tracer, or normalization species, it can be
deselected by highlighting the species in the left-hand box and selecting the
same button again. Thus, if a species is set as a tracer and no tracer is desired,
then it can be deselected by highlighting it and selecting the Tracer button.
Specific examples of using the total, tracer, and normalization options for VOCs
and PM can be found in Mukeriee et al. (2004), and Lewis et al. (2003).
3.3 Initial Species
Unmix requires the selection of species from the input file for the model.
Selected species can be determined by the user or by using the Unmix Species
Selection Tools. The Select Initial Species command uses the species with the
largest loadings in the varimax factor analysis of the data to find a selection of
species that gives a 4 or 5 source model that has very good signal-to-noise
properties. If a 4 or 5 source solution is not found, a 3 source solution is
attempted.
Before using the Unmix Species Selection Tools, move the species with high
mean mass concentration over to the Species box. For example, select the
species with a mean mass concentration greater than 1 |j,g/m3. Select the Data
Processing button in the upper right corner of the main window to go back to the
Data Processing window in order to review the data. The species with mass
concentrations greater than 1 ng/m3 in the wdcpmdata are MF, EC, EC1, N03,
OC, and S04 (species means are shown in the Data Processing window). Other
species such as SI could be added, since it is a marker for soil or crustal material
and it is typically present in quantities above the analytical method detection limit
(XRF). Select the OK button to return to the main window. Note that you can
track when species are designated as Total, Tracer, or Norm in the bottom right
corner of the main window. In the current example, Figure 6 shows that the
species MF is designated as Total and Norm. In order to view the results as
mass fractions, highlight MF, and select the Total and Norm buttons. Select the
first Species Selection Tool which is the Select Initial Species command shown in
Figure 6.
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
-itUnselected Species
ercent of Species Vs. Total
Factor Analvre selection;.
Analyze Run I Highlight Run Output I Diagnostic Pints
Figure 6: Select Initial Species
The Analysis Results window (Figure 7) shows the Unmix solution with the added
species. A 5 source solution was found by adding Al, OC3, OC4, and SI to the
initial list of selected species. In addition, the species are automatically moved
from the Unselected to Selected Species box in the main window as shown in
Figure 8. If an error message is displayed stating "Factor Rotation did not
converge", the user should replace zero's or negative values in the input data set
with a missing value code. The Replace Missing Data command in the Data
Processing window can be used to replace the values before running Select
Initial Species.
The preamble to the Unmix results is pretty much self-explanatory. The line that
gives the Min Rsq, etc. does require some explanation. Min Rsq is the smallest
r-squared value for any species in the model (r-squared for any species is
greater than this value). The Min Sig/Noise is the smallest estimated signal-to-
noise ratio of any of the factors included in the model.
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EPA Unmix 6.0 Fundamentals & User Guide
•) Analysis Results EPA Unmix 5.0 - |fn](x]
Tools
Analysis Results
SolK 0.0 0.09 0.04
PB 0.1 0.06 0.23
SE 0.1 0.26 0.09
SI 0.2 0.06 O.OS
S04 0.9 0.11 0.09
TI 0.3 0.15 -0.01
V 0.00. 19 0. 13
ZH 0.0 0.24 0.34
1 S04
2 OC3 OC4
3 EC1 EC
4 AL SI
6 H03
7 EE
e oci
9 AS
10 SolK K
1 TI
1 BR
1 HI
1 V
1 ZH
1 CA
2 FE CU
* **** Run * 1 ******
T TAL: HF
H rmalizacion: HF
nmix Source Compos tion
H 2.6
E O.OZ9
H 3 0.4S
0 0.094
ELAPSED TIME = 0 MIHUTES
0.03 0.00 0.02 0.01 0.03 0.0 0.96 0.04 0.01 0.02 0.04 0.06 0.01 0.01 0.09 0.0 0.02 -0.00 0.00 0. A
0.02 0.00 0.12 0.08 0.07 0.2 0.44 -0.02 O.OS 0.06 0.16 0.07 0.17 0.01 0.77 0.0 0.06 -0.00 0.03 0.
0.02 0.00 0.11 0.91 0.06 0.0 0.02 0.04 0.17 0.11 0.02 0.07 O.OS 0.01 O.OS -0.0 0.02 -0.00 0.01 0.
0.93 0.00 -0.04 -0.01 0.03 0.0 0.00 0.04 -0.01 0.06 0.03 -0.01 0.00 0.02 0.01 0.2 0.08 -0.00 -0.03 -0.
0.18 -0.07 -0.03 0.09 0.02 0.0 0.04 0.09 0.00 0.03 0.02 0.00 -0.00 0.00 0.04 0.0 -0.01 0.01 -0.00 0.
0.47 0.00 -0.03 0.03 -0.00 0.1 0.21 0.70 0.01 0.24 -0.06 0.05 -0.01 0.02 -0.03 0.08 0.14 -0.00 0.02 0.
O.OZ 0.00 0.15 0.10 0.06 0.0 0.17 0.03 0.11 0.15 0.3B O.S3 0.09 0.01 0.06 0.00 0. 03-0. 00 O.OZ 0.
-0.01 0.00 0.27 0.12 0.09 0.1 0.06-0.01 0.14 0.17 0.23 0.15 0.69 0.00 0.25 0.07 0.17 0.00 0.04 0.
g/Hoise= 4 . 32
7.02 1.07 2.98 2.88
0.0334 0.033 0.261 0.0605
0.00519 0.0103 0.0636 0.0303
0.0732 0.1 O.Z53 0.4S4
0.5 SECOHDS
Figure 7: Initial Species Source Profiles
Select the main Unmix window to view a summary of the results. The Solution
Summary box displays the summary information for the run. The highlighted line
in the Solution Summary box tells us that there are 10 species and that there are
1171 observations. In addition, the r-squared values and the signal-to-noise
ratios are listed for the run. In the example above, the data can be explained
with a five source model with a minimum r-squared value of 0.98. This means
that at least 98% of the variance of each species can be explained by five
sources. Thus, the number in the Unmix display is the minimum r-squared value
over all the species, not the overall r-squared of the fit. The run type is "I" for
individual runs or "B" for batch mode (see Section 7). The signal to noise ratio is
calculated by a procedure known as NUMFACT, which is described with several
examples in Henry etal. (1999). The minimum number of sources is 3 and the
recommended number of sources in the # Sources for the Current Run box is
determined by the NUMFACT algorithm. The maximum number of potential
sources is the number of sources with a signal-to-noise ratio greater than 1.5
(Analysis Diagnostics box). The user may see slightly different values for r-
squared and signal-to-noise than those shown in Figure 8 because of the Monte
Carlo nature of the underlying calculation. The user may wish to override the
automatic selection and enter a new number of sources between 3 and
maximum number of sources in the # Sources for the Current Run entry box.
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EPA Unmix 6.0 Fundamentals & User Guide
Run ## Species if Qbs # Sources Min. Min. Run
Rsq SigMoise Type
Figure 8: Initial Selected Species
3.4 Suggest Additional Species
The Suggest Additional Species command is used to create a list of species that
can be added to an Unmix solution. Select the second Species Selection Tool,
Suggest Additional Species command as shown in Figure 9. Select the All
option to run both the SAFER and Influential Points (IP) Algorithm. Select the All
button to run both the SAFER and Influential Points (IP) algorithms (see Section
5.2) and use the default spread parameters for the IP. The window shown in
Figure 10 will appear after the SAFER and IP progress bars are displayed.
Please note that selecting both the SAFER and IP can take a while to calculate
depending on the number of unselected species and data observations.
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Select AnaKoi- Selected species Tools
FitUnselected Species
Percent of Species Vs. Total
Factor Analyze Selections
Figure 9: Suggest Additional Species
14
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EPA Unmix 6.0 Fundamentals & User Guide
Ueighte
Score
0.7141
0.5519
0.5295
0.4513
0.4460
0.3598
0.2931
Haas
6.5578
7492
3193
1507
9853
2.2137
2.7130
To select species, highlight desired species on lines below before pressing the "Select" pushbutton
Based on influential point algorithm,
the following species are suggested
in the order of the listing
Edge Resolution Details (percentiles)
90th 50th # Influential Points
0.807
0.546
0.698
0. 648
0.834
0.818
0.447
0.567
0.346
0.282
869
0.867
0.788
762
D.730
0.621
Figure 10: Suggestion Species
If the SAFER algorithm cannot suggest any additional species to add, only the
influential species information will be displayed. Choose additional species by
selecting the species in the list below the "****" line. Select species from the
SAFER Algorithm that have a Max Signal to Noise (Max Sig/N) greater than 2
and Minimum Signal to Noise (Min Sig/N) less than 1. If a TS was selected, the
SAFER Algorithm output also includes columns labeled Big Mass and Big Mass
Percent. The idea is to distinguish between species that contribute to sources
that explain only a small amount of TS. Assume two species explain 4 percent of
the TS on average. However, the source contributions for one of the sources are
sometimes very big, in fact sometimes this "small" source explains over 40
percent of the mass. A solution with such a source is to be preferred to a
solution with a source that is always there but at a low level. In addition, it is
recommended to select species from the Influential Point Algorithm that have a
high edge resolution (90th percentile greater than 0.80) or a low number of
influential points.
The Suggest Additional Species command can be run multiple times by
evaluating the species with the highest Weighted Score in the Unmix solution. If
a feasible solution is found after adding the species to the Selected Species, use
the Analyze Run, Fit Diagnostics command to evaluate the solution. For this
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EPA Unmix 6.0 Fundamentals & User Guide
example the following species are recommended: Se, Ca, and Si. If the number
of significant and strong species abruptly decreases after adding a species,
remove the species from the selected species box, and either try the next
recommended species or finish using the Suggest Additional Species command.
This process has been automated and is available by selecting the Auto Unmix
(AU) command.
Another option is to select multiple species based on the SAFER Algorithm,
Influential Points Algorithm, and species that are useful for identifying sources
such as Se for coal combustion. However, selecting multiple species may result
in a non-feasible solution. Select species that are components of potential PM
sources in Washington DC: K (crustal, wood smoke), SolK (wood smoke), and V
(residual oil) (Figure 10). The species will be highlighted in the Unselected
Species box. Select the <- button to move the species to the Selected Species
box and select the Run button. A new 7 source solution is displayed in the
Analysis Results window (Figure 11). Two additional Unmix options are available
for selecting additional species: Auto Unmix (AU) and Batch Mode. These
options are discussed in sections 4 and 7.
.' Analysis Results - EPA Unmix 6.0
Analysis Results
n the order of Che listing
-Jan-2007 12:15:07
le: C:AProgram FilesAEPA Unmix 6.QAData\wdcpiidata.txt
acer: Hone
TAL: MF
realization: HF
n Esq - "o_93, Min'sig/N
timix Source Composition
0. 01
O.OD124 0.000589
0.6 0.000673
0.0809 0.0772
0.0242 0.00888
0.2B3 0.0052 Q.OD90S 0.00281 0.00441
0.1Z4 0.0698
LAPSED TIME = 0 MINUTES 2.2 SECONDS
ill
Figure 11: Suggest Additional Species Source Profiles
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EPA Unmix 6.0 Fundamentals & User Guide
3.5 Plot Distribution
Select the MF line of Run # 2 from the Analysis Results window and select the
Tools, Plot Distribution command to create a pie chart showing the average
source contributions (Figure 12). The secondary sulfate source (source 2)
contributes 44% of the MF or PM2.5. The color bar and legend can be
added/customized and the figure can be saved.
OTAL:
3 Spe
in P.S
tmix
F
, 1171 Obs., 7 Saurc>
O.S8, Min Sig/Nois
ce Composit-ion
Source *3«1%
Distribution of sources for MF in Run #2
Source*! -13%
Source #7-16
Source #2 -44'
Source iM -5%
Figure 12: Analysis Results - Plot Distribution
3.6 Evaluating Results
An individual run can be evaluated by selecting one of the buttons below the
Solution Summary box in the main Unmix window: Analyze Run, Highlight Run
Output, or Diagnostic Plots. The Highlight Run Output option highlights the
solution in the Analysis Results window. The Analyze Run window, shown in
Figure 13, lists outputs that can be exported to the Analysis Results Window, text
file, or Excel file. The predicted results from Unmix can be calculated by adding
the Selected Species Data and Species Residual Files in Excel.
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EPA Unmix 6.0 Fundamentals & User Guide
Select Analyze Selected bpecies Tools
Selected Species
Unselected Species
tidbs
Input Data Processing
1173
1197
1193
1195
1199
1199
Analyze Run - EPA Unmix 6.0
Export Content
Analysis and Export of Run Results
Help
Q Data Processing Report FJ Input Data Used In this Run
Results
f_J Source Composition
fj Source Contributions
Evaluation
Source Composition Species
D Variability fj Fit Diagnostics
fj Variability Distribution FJ Residuals
Source Contribution fj standardized Residuals
Q Correlation
FJ Select All of the Above
Destination
0 Analysis Results Window
O Text File
O Excel File
Export
Analyze Run
Highlight Run Output
Figure 13: Analyze Output window
Fit Diagnostics example output is shown in Figure 14. The diagnostics include
the regression statistics between the predicted and measured species
concentrations, whether any species have a significant negative bias,
strong/significant species in a source, and details on the variability distribution. If
a normalization species was selected, the source contribution output will be for
the species. For example, if PM was selected as the normalization species, then
the source contributions output will contain PM source contributions for each
sample.
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EPA Unmix 6.0 Fundamentals & User Guide
Analysis Results EPA Unmix 6.0
Analysis Results
SI 0.93
304 1.00
V 1.00
Total Variable:
HF 0.93
0.02
-0.00
0.00
0.04
0.33
0.00
0. 90
1.00
1.00
-0,00
0.01
-0.00
0.95
1.00
Bootstrap Details
Block Length: 31 (Ease Data Auto
relation: LOW)
Negative Bias
Strong - EC, SQ4, V
Significant - K, HQ3, OC, OC3, OC4, SoJLK
Source 2
Strong - SolK, V
Source 3
Strong - Hone
Significant - Hone
Strong - AL, K, OC, QC4, SolK, V
Strong - V
Significant - AL, EC, EC1, K, H03, OC, OC3, OC4, SolK, SI, S04
Figure 14: Analysis Results - Fit Diagnostics Example
It should be noted that Unmix can generate results with negative concentrations
for species and the TS. The occasional small negative value is due to the effects
of errors. Allowing for small negatives is necessary to reduce bias in estimating
source compositions for species that are zero or very small. If a species is
significantly negative, it is recommended that the species be removed from the
Selected Species box. Reducing the number of sources in the model generally
results in a solution without a negative TS. The Fit Diagnostics and guidance on
interpreting the output is shown in Table 2.
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EPA Unmix 6.0 Fundamentals & User Guide
Table 2: Fit Diagnostics Guidance
Fit remaining
species
Correlation,
differences, and
regression
coefficients
Bootstrap Details
Negative Bias
Significant/Strong
Species
Species Report
Try adding species with
at time, to the Selected
that will add meaning to
rA2 greater than 0.80 in descending order, one
Species box and run Unmix. Select species
the existing profile.
Evaluate species with low rA2 values (< 0.30) or with greater than 1
outlier for 100 points using the View/Edit Points and Observations
tools. If species still have rA2 values less than 0.30 and do not
significantly aid in the interpretation of the profiles, remove the species
from the Selected Species box.
After evaluating the bootstrap variability percentile summary in the Fit
Diagnostics and the Diagnostic Plots, Variability Distribution option,
use the following guidelines for the number of attempts to obtain 100
feasible solutions.
Data Set Size
> 600 samples
400 - 600 samples
< 400 samples
# of attempts to obtain 100 feasible solutions
(rough estimates only)
Up to 140
Up to 150
Up to 160
Species with significant negative bias should be evaluated in more
detail using the View/Edit Points and Observations tools. Remove any
species from the Selected Species box with significant negative bias.
Strong Species have a contribution to a source that is greater than or
equal to 1 times the standard deviation of the bootstrap estimated
variability (sigma). Significant species have a contribution to a source
that is greater than or equal to 2 times sigma. Most sources should
have both strong and significant species, with the significant species
having large signals-to-noise ratio. Look for reasonableness of the
profiles and how species group. Only one or two sources should have
neither significant nor strong species.
Values
0
1
2
+
Interpretation
Base run source profile value not contained in
the IQR.
Base run source profile contained in the IQR
but not centered.
Base run source profile contained in the IQR
and is centered.
2.5tn percentile value of source profiles from
the bootstrap runs > 0
IQR - interquartile range, between the 25th and 75th percentile.
Interpretation of species in source variability percentiles should focus
on species with little influence of outliers (2+). Species not strongly
influenced by outliers are a 1+ and should be interpreted. Species that
are impacted more by outliers are 0, and generally have low
contributions to a source and should be interpreted with caution. Total
Mass species should be category 1+ or 2+, however, a source with a
total mass summary value of 1 is acceptable because the source may
explain species variability without having a significant contribution to
the total mass. Each source should have multiple 1+ species.
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EPA Unmix 6.0 Fundamentals & User Guide
In the main Unmix window, select the Diagnostic Plots button. The Diagnostic
Plots window contains many plotting options and an example from the Fit
Diagnostics option is displayed in Figure 15. The predicted vs. measured
concentrations are shown in the top plot and the regression results are shown in
the bottom plot. A figure is generated for each of the selected species. Use the
« Previous (Prev) and Next » buttons to view each of the figures.
Diagnostic Plots - EPA Unmix 6.0
Undock Figure I Figure Groups
Diagnostic Plots for Run Number 2
— Predicted Cone.
Measured Cone.
Run number2: Predicted and Measuted Concentrations of MF
/ /• ,/ y ^ ^
Scatter plot of Predicted Vs. Measured Cones with the linear fit Eqn: y = 1.01 x-0.15, r2 Value - 0.96
G Fit Diagnostics
G Standardized Residuals
10 15 20 25 30 35 40 45 50
Plot Options
G Source Composition
G Source Contribution
Evaluation
Source Composition
G Signal-To-Noise
G Confidence Interval
G Variability
G Variability Distribution
G Edge Plot (Source Contribution)
Base Source:
Species
Figure 15: Diagnostic Plots - Fit Diagnostics Example
The majority of the options in the Analyze Run and Diagnostic Plots window are
self-explanatory and a Help button is available for details. Some explanation is
required for the Source Contribution plots: Normalized scale plots have source
contributions that are scaled to range between 0 and 100, Uniform scale plots
have source contributions that are scaled to range between 0 and 1, Actual scale
plots are not scaled and these plots will display the true source contribution
values.
In addition to evaluating the Fit Diagnostics plots, the standardized residuals
should be evaluated by selecting the Diagnostic Plots, Standardized Residuals
option. The standardized residuals from residuals (difference between predicted
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EPA Unmix 6.0 Fundamentals & User Guide
and measured concentrations) are calculated by first mean centering the
residuals and dividing the result by the standard deviation of the residuals.
The standardized residuals distribution should appear similar to the standard
normal distribution (zero mean and standard deviation of 1) with the majority of
standardized residuals should be between -3 and +3. Species with significant
number of standardized residuals outside this range should be evaluated in more
detail using the Data Processing window under View/Edit Points and
Observations options.
The figures can be saved using the Save button. If many pages of figures are
saved using the Save All button, the figures are automatically named with the
figure type followed by the figure number (i.e. Source Composition_fig_1). These
figures can be grouped together in one file using Adobe Acrobat's Create PDF
"From Multiple Files" option.
3.7 No Feasible Solution
Unmix looks for edges in a multidimensional plot of the data. If N sources are
sought, Unmix needs to find N edges. From each edge, the normalized source
contributions of a source can be estimated. If fewer than N edges are found,
earlier versions of Unmix simply reported "No Feasible Solution", even though it
may have found N-1 edges. Unmix also reports "No Feasible Solution" if N or
more edges are found but these lead to source compositions that have negative
source contributions that are too large or too numerous. Again, earlier versions
only reported "No Feasible Solution" even though information was gathered
about the sources. Unmix 6.0 reports estimates of partial solutions and other
information in order to give more guidance to the user to produce a better
solution.
The nature of the partial solutions reported by Unmix depends on the number of
edges found and whether or not a total species has been set by the user. In the
following, 'edge' and 'possible source' are used interchangeably. When no
feasible solution is found, there are three possible types of partial solutions.
• If a total species is not set, Unmix reports the species that have a
correlation > 0.8 with the contributions associated with the edge. If there
are no such species, 'None' is reported.
• If a total species is set, the behavior of the solution depends on the
number of edges found. If the number of edges is < the number of
sources, Unmix does a complex calculation to estimate the percentage of
the total associated with each possible source (edge). Unmix reports the
estimated total percentage and the species that have 50% or more of their
average concentration explained by the edge. If there are no such
species, 'None' is reported.
• If the number of edges is > the number of sources, Unmix reports the
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EPA Unmix 6.0 Fundamentals & User Guide
correlation of the total species with the possible source and the species
that have a correlation of > 0.8 with the possible source. If there are no
such species, 'None' is reported.
A partial solution is generated when Cu, and Zn are added to the selected
species shown in Figure 8. Seven sources are listed with major species (Figure
16). The largest possible source is secondary sulfate with MF and S04 (44%).
Other possible sources are nitrate (N03), crustal (Al, SI), motor vehicles (EC,
EC1), Zn, and Cu sources. One source was also identified that has no major
species.
Analysis Results - EPA Unmix 6.0
I Tools
Analysis Results
H03
S04
0.0433
0.216
0.0237
0. 538
0. OZ43
0,356
0.0315
0.165
0. 155
0.0933
ELAPSED TIME = 0 HIMUTES 6.5 SECONDS
*** Run # 2 ******
WARNING HO SOLUTION - HOT ENOUGH CONSTRAINTS. NUMBER OF FACES
TOTAL: HF
nalization: HF
NO FEASIBLE SOLUTIO
Selected Species
HF
AL
3.41
16.21
£.17
44.41
6. 94
13.39
Figure 16: Partial Solution
3.8 Estimate Source Profile Uncertainties
The variability of the base run, commonly referred as uncertainties in source
profile, are estimated using a block bootstrap method. A note on the use of the
terminology used is necessary. Source Profile Uncertainties is a phrase generally
used by researchers to evaluate the robustness or the stability of a chosen
source profile. The source profile is considered robust or stable if small changes
to the input data produces proportionally small change in the results. In essence,
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EPA Unmix 6.0 Fundamentals & User Guide
the bootstrapping technique helps measure the variability in the source profile
produced by the variability in the input concentration data. However, it is
important to note that variability and uncertainty are not technically equivalent.
Variability is a point estimate of the uncertainty just like the mean being a point
estimate of the distribution. Uncertainty associated with the source profile can be
constructed only by running multiple block bootstrap runs on the same same
source profile. This is similar to the process of collecting samples (eg. Number of
hurricanes to hit Florida in September) to be able to construct the underlying
unknown distribution. In other words, uncertainty is the distribution associated
with the sample space of variability.
Bootstrap data sets are constructed by sampling, with replacement, from the
original data set. This randomly re-sampled data may not retain the positive
serial correlation of the original, which could lead to errors canceling out when
they should not. The solution is to break the original data into blocks of data that
are long enough to retain the serial correlation. The bootstrap samples are
obtained by re-sampling the blocks of data with replacement. Blocks of data are
chosen until the new data created has the same number of observations as the
original data. This data set is then used as the input to the Unmix. Since, there
is no guarantee of a feasible solution for every bootstrap data set, bootstrap data
sets are created and run until one hundred feasible solutions are obtained. They
are used to calculate the standard deviation (or sigma) and percentile distribution
of the source compositions. The variability computation algorithms are described
in detail in Appendix C.
The singular value decomposition of the bootstrap sample is calculated and the
duality principle translates the known (normalized) source contributions into
edges in the bootstrap sample's principal component space, called the bootstrap
V-space. These edges are used as initial guesses to find edges in the bootstrap
V-space. After finding these new edges, everything is the same as in basic
Unmix with one exception. Occasionally if there is a lot of error or outliers in the
data, the initial guesses (as good as they are) do not converge on a new edge. If
this occurs, the Variability Algorithm will generate a different initial guess to look
for the edge.
Variability or uncertainties in the source compositions are estimated for feasible
solutions by selecting the Analyze Run button, Variability option. The Analysis
Results Window will display three types of variability distribution diagnostics for
each source. The first one is the sigma, and the composition divided by 2 times
sigma. The composition divided by 2 times sigma represents the signal to noise
ratio and is greater than 1 for species that contribute significantly to a source.
The next is the set of percentile values on the range of bootstrap run values. The
2.5th to 97.5th range in percentiles is an estimate of the 95% confidence interval
that accounts for the non-negativity constraint in Unmix. Finally, a new method is
used to provide a 90% and 95% confidence intervals. This method provides the
range of bootstrap run values as a percent of the base run value and centered
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EPA Unmix 6.0 Fundamentals & User Guide
about the base run values. We will refer to this as the Discrete Difference
Percentile (DDP) method and its algorithm is described below.
Before describing the DDP method, we will provide the justification for
introducing a new metric. While the first two methods (Sigma and Percentile)
provide a statistical overview of the nature of the bootstrap runs, neither method
provides a reportable statistic that connects the source profile that is being
evaluated to the summary information provided by those methods . The sigma
method provides the variation about the mean whereas the percentile method
provides an insight in to the spread about the median values of the bootstrap
source profiles. But, there isn't a clear method to compare the mean nor the
median of the bootstrap source profiles to the chosen source profile under
investigation. The DDP method is designed to address these shortcomings.
The DDP method contains the following steps. The procedure is applied to each
entry in the source profile matrix.
1. For the chosen entry in the source profile matrix, collect the corresponding
entries in the bootstrap matrices.
2. Construct the absolute difference values by taking the absolute value of the
difference between the chosen source profile entry and the corresponding
entries in the bootstrap source profile matrices.
3. Compute the 90th and 95th percentile value of the collected absolute
difference values.
4. Repeat this process for each entry in the chosen source profile matrix.
For example, the second source shown in Figure 11 (secondary sulfate) has a 95
% confidence level value of 4% for S04 with the mass fraction value of 0.55 (MF
specified as normalization species). The 95% confidence interval using the
ranked value metric states that 95% of the bootstrap source composition species
mass fraction lies between 0.53 (0.55 - 4%*0.55 = 0.55 - 0.02) and 0.57 (0.55 +
4%*0.55 = 0.55 + 0.02). If a normalization species is not used, the confidence
interval can be calculated using the example shown above. Relative source
contribution values are typically reported for PM studies and if a normalization
species is specified the ranked value output also provides the percent and
confidence intervals. For source 2, the MF percent is 44 and the relative 95%
confidence interval is 8%. The contribution of the secondary sulfate to MF or
PM2.5 is 44 ± 8%.
The advantages of the DDP method over the other two methods are two-fold.
Firstly, the method gives an exact quantity that describes the variation about the
base run source profile which is exactly the quantity that is being evaluated and
not the variation about the mean or the median of the bootstrap source profiles.
Second, the use of percentile to predict the variation about the base run source
profile is a statistical value and not a value tied a specific set of bootstrap runs.
The use of sigma to describe the variation is one such case where the
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EPA Unmix 6.0 Fundamentals & User Guide
descriptive value (sigma) is tied to the specific bootstrap run and may vary from
one bootstrap run to another. Nevertheless, the user should use all the available
inferential information to evaluate the base run source profile. If, in particular, the
conclusions to be drawn from the three methods vary significantly, the user
should attempt to explain the possible implications of the differences while
reporting the results.
It is recommended that the DDP method output, at the minimum, be included in
any reports or publications to summarize the source profile variability associated
with a base run source composition. Also, the user is advised to choose the 90%
confidence level for small and/or noisy data set and 95% for medium and large
data sets (greater than 250 observations).
The variability information can also be viewed graphically by selecting the
Diagnostic Plots button, Confidence Interval option. The plot displays the 2.5th to
97.5th percentile range and the source profile composition is shown by an
asterisk (*) for each source. If a 2.5th percentile value is negative, it is displayed
as 10~4 in the plot (see Section 3.6 for a discussion of small negative values). An
Variability Estimate Plot for the source profiles is shown in Figure 17.
Undock Figure III Figure Groups
Diagnostic Plots for Run Number 2
Source composition variability error for run #2 - Log Scale.
Help
t
;
;
t
:
F :
:
•
-
_,
;
;
3
'.
E 3
=
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t
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=
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-
Plot Options
G Source Composition
G Source Contribution
Evaluation
Source Composition
G Signal-To-Noise
0 Confidence Interval
O Linear >:/) Log
n Variability
G Variabilrry Distribution
Q Edge Plot (Source Contribution)
Base Source :
G Fit Diagnostics
G Standardized Residuals
Figure 17: Variability Estimate Plot
26
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EPA Unmix 6.0 Fundamentals & User Guide
The source profile variability plots should be evaluated before interpreting the
source profiles. Select the Diagnostics Plots, Variability option and two subplots
will be generated for each source as shown in the following figure. Use the Next
button to view the other 6 sources.
,' Diagnostic Plots - EPA Unmix 6.0 - \\O\\X\
File
|»l""™l Diagnostic Piots for Run Numbers I™"1
100
80
s 6D
1 40
20
0
10'
10°
10"'
•; 10-'
I "•<
io-4
io-5
Percent of Species Apportioned to Source # 1 of the Chosen Base Run
i
1
+ +
""*" ^ =*= A 4s ^ i
.*.=*=•#- 2*3 * TT f tp ^. - -*-_
4 * * #• * ^ & j> „'-- / * #*
Fraction of Species Apportioned to Source # 1 of the Chosen Base Run
• 4 i * * * > + * :
: i ' ^ * * i *:
+ ilii+ | + +J_ T
^ <^ * #• •*• ^ -f ^
Help
Plot Options
Results
G Source Composition
G Source Contribution
Uniform
Evaluation
Source Composition
G Signal-To-Noise
G Confidence Internal
0 Variability
G Variability Distribution
G Edge Plot (Source Contribut on)
Base Source :
Species
G Fit Diagnostics
G Standardized Residuals
Generate Plots
«Prew Hext»
1 Exit
Figure 18: Source Profile Variability Plot
The first subplot titled "Percent of Species Apportioned to Source #1 of the
Chosen Base Run" displays the variability in the percent of the species
apportioned to the currently viewed source. The figure is generated as follows.
1. If the chosen base profile contains M species and N sources, then the
bootstrap matrix will of the dimension M x N x 100, where 100 equals the
number of feasible bootstrap runs that are used to plot the above figure.
Each box plot in the figure above uses 100 data points for the each
species and source. There will M box plots per subplot, one for each
species and N sets of subplots, one for each source.
2. For each bootstrap run, the bootstrap matrix is normalized using the row
01 im
sum.
3. The base run profiles are also normalized by their row sums.
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EPA Unmix 6.0 Fundamentals & User Guide
4. The values for each species and source over all the bootstrap runs are
then used to construct the box plot figure. The normalized values from the
base run are marked by "*" in the subplot.
5. The red pluses represent the outliers in the plotted data set.
The first subplot highlights species that contributed to the source. In other words,
the higher valued species in this subplot are candidates that highly influenced
this source in its composition. It should be noted that the pie chart percentages
in Figure 12 may not match the percent of species attributed to a source since
they are source contribution (profile x source contribution) and profile based
calculations, respectively.
The second subplot represents the same bootstrap matrix using a slightly
different metric. The procedure used to plot the bottom subplot is as follows.
1. Similar to the top plot, each box plot in the figure uses 100 data points for
the each species and source, M box plots per subplot, one for each
species and N sets of subplots, one for each source.
2. For each bootstrap run, the bootstrap matrix is normalized using the
column sum. The base run source profile is normalized the same way.
3. The normalized values are used to plot the box plot. Due to this
normalization, the y-axis limits will always range between 0 and 1.
Therefore, the axis is marked in logarithmic scale to highlight the species
with smaller values and ranges. The normalized profiles are marked by "*"
as in the top subplot.
4. The species titles for which the normalized profiles do not fall within the
inter-quartile range are shown in a red outlined box (see SI in the second
subplot in Figure 18).
The first subplot in Figure 18 highlights N03 as being the largest significant
contributors to Source 1. The subplot matches well with the output from the
sigma-based output shown in Figure 14 which listed the significant species
contributing to Source 1 were K, N03, OC, OC3, OC4, and SolK.
The second subplot shows the variation in the species apportionment. This
subplot should be mostly used to confirm inferences from the first subplot. For
instance, an influential species from the first subplot may be confirmed if their
variations are not too large in the second subplot. The vice versa may hold true
in some cases. An influential candidate may be rejected if their variations appear
to be larger than expected in the second plot
Nevertheless, in both cases, the user should use all available information before
arriving at a conclusion. This includes the information of known local sources,
data set anomalies, and other inferential data provided by the model. As is true
with any chosen method, certain data are favored more than the others. The
user should be aware of the limitations and adjust their conclusion accordingly.
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EPA Unmix 6.0 Fundamentals & User Guide
The second subplot in Figure 18 shows that the SI contributing to Source 1
should be interpreted with caution since the variability is significantly higher in the
second subplot compared to the first and the presence of many outliers. This
species is shown in a red outlined box because the base run "*" is not within the
IQR. In these cases, the user should use other available information such as
local emission inventory and/or measured source profile information and ensure
that the output from the model is not over-interpreted. Source Profile Variability
is an invaluable tool that helps prevent the model from identifying incorrect or in
some cases non-existent sources.
The second subplot results in Figure 18 are summarized in tabular form in the
Analyze Run, Fit Diagnostics option (see Figure 19). The ranking goes from 0 to
2 with 0 being highly suspect to 2 being the ideal. Along with that, the presence
of the "+" sign indicates the non-negative nature of the 2.5th percentile value of
the source composition value from the bootstrap runs.
Analysis Results
Strong - EC, SQ4, V
Significant - E, H03, QC, OC3, QC4, SolE
Source 2
Strong - SolK, V
Significant - AL, EC, EC1, K, OC, OC3, DC'
Source 3
Strong - None
Significant - None
Source 4
Analysis Results
Significant - EC, EC1, H03, S04
.rce 5
Strong - EC, EC1, OC3, V
Significant - AL, K, OC, OC4, SI, S04
.rce 6
Strong - V
Significant - AL, EC, BC1, E, N03, OC, OC3, OC4, SolE, SI, S04
.rce 7
Strong - S04
Source profile HOT
Figure 19: Species Report (percentile based)
The distribution of the variability estimates should be evaluated for small or
medium size data sets (less than 600 observations) or data sets that contain
infrequent high species measurements. Select the Analyze Run button, and the
29
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EPA Unmix 6.0 Fundamentals & User Guide
Variability Distribution option. A table is generated that shows the profile and
variability, the results of 4 independent runs of the variability estimate, and the
coefficient of variation (CV) of the species uncertainties. The results can also be
plotted by selecting the Diagnostic Plots button, Variability Distribution option.
The ratios of the variability estimate to the profile value are plotted for each
species and source.
The variance of repeated variability estimates should be evaluated before
selecting a final solution. This evaluation is especially important for small data
sets (< 250 observations) and for data sets that have infrequent impacts by
sources. The coefficient of variation (CV %) of uncertainties from the selected
run and four additional runs is determined by selecting the Analyze Run button,
Variability Distribution option. A CV less than 25% is preferred for each of the
species in a source; however, some species that are at concentrations near their
analytical method detection limit may have higher CV values. The results can
also be plotted as a ratio of the variability distribution to the species concentration
by selecting the Diagnostic Plots, Variability Distribution option.
These plots display the spread of sigma values obtained from 5 variability
estimation runs. The individual variability values are normalized to the median
variability so that the median value of the transformed values of the sigma values
from the variability runs is always 1. The plots show the distribution of the
normalized values with the red lines ranging from the normalized minimum to the
normalized maximum values. The blue star denotes the normalized median
values and is always present at 1. The data related to any species that shows a
large spread should be analyzed thoroughly.
3.9 Run Profiles
Run profiles or selections can be saved using the Save Profile command as
shown in Figure 18. The profiles are saved as .umx files that can be opened and
edited in Microsoft Excel. The default folder for these files is C:\Program
Files\EPA Unmix 6.0\Unmix Profiles. Using the data and selected species shown
in Figure 11, select the File and Save Profile commands and save the file as
wdcpmdata profile.umx.
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EPA Unmix 6.0 Fundamentals & User Guide
Run # * Species # Obs # Sources Min. Win. Run
Rsq SigJNoise Type
Analyze Run I Highlight Run Output I Diagnostic Pints
Figure 20: Save Current Run Choices
The umx file can be opened by starting Microsoft Excel, selecting the File and
Open commands, changing the directory to the C:\Program Files\EPA Unmix
6.0\Unmix Profiles folder, and changing the file name extension to *umx. After
selecting the wdcpmdata profile.umx file, the following spreadsheet will open
(Figure 19). To reload the run profile information into Unmix, select the File and
Load Saved Profile commands from the main window in Unmix.
31
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EPA Unmix 6.0 Fundamentals & User Guide
D Microsoft Excel wdpmdata profile. UNIX
File Edit View Insert Format Tools Data Window Help Adobe PDF
.3du.AUaaH *> -1 £ -miIB ™°'° "ifel '=Arid
Type a question for help
m/ u sfflsrai $
T _ ff X
- B
'••-I
A1 - f* EPA Unmix B.O Model Run Input Details
1
2
A | B
c
D
EPA Unmix 6.0 Model Run Input Details
3 Caution: Please do not alter the fimn.it. Altering the finin.it will lead to ncoirect inputs to the piogiam and eventually crash the executable.
4 Please eutei the values in the allotted space only.
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
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27
28
29
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Input Data File Name:
Replaced Missimj Value
Missing Value Symbol
Dates Hours Included
Removed Data Rows
C:\Program Files\EPAUnmix6.0\Data\wdcpmdata.txt (Last Modified: 01-Jun-2006 16:35:26)
No
0
Dates only
Total
Tracer
Norm
MF
None
MF
CAUTION: Make sure that the same species appears once and only once in the species columns.
Unselected Species
AS
BR
CA
CU
FE
MN
N]
OC1
OC2
PB
SE
Tl
ZN
Selected Speices
MF
AL
EC
EC1
K
NO3
OC
OC3
OC4
SolK
SI
S04
V
Replaced Species
Excluded Species
CL
CR
EC2
ECS
NA
OMC
OP
S02
SR
ZR
arnrriNu"!
ammS04
E T1
V
H <
Ready
M \EPA Unmix 6.0 Input Sheet/ Input Data / Old Source Contribution / Deleted Points / | <
Figure 21: Umx File
SECTION 4. AUTO Unmix
Auto Unmix (AU) works by finding an initial model with the species selected using
a varimax-rotated factor analysis of the data. The remaining species are added
one at a time looking for new models with one more source than the initial or
base model. Each new model found then becomes a base model, and the
process of adding the remaining species one at a time is repeated. For each
group of models with N sources, a model Figure of Merit (FOM) between 0 and 1
is calculated, with a FOM of 1 representing the best possible model. Eventually,
the process ends when adding new species does not give new models with more
sources. At this point, the uncertainties in the source compositions are
calculated and models with too much variability (as defined below) are
eliminated. Finally, a new modified FOM is calculated, and the models are
stored in order of decreasing FOM.
The FOM calculation depends on whether a TS such as PM2.s has been
selected. It is strongly recommended that TS be selected in the data since it
makes ranking the models more reliable. The amount of TS explained by each
source is as an important part of the FOM calculation, and if no TS is selected,
32
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EPA Unmix 6.0 Fundamentals & User Guide
then AU uses a similar method to calculate the FOM that leaves out the parts
that require TS.
Assume that one or more base models with N-1 sources have been found.
Further assume that adding remaining species one at a time to the base models
results in K new models with N sources. The FOM is calculated as a weighted
sum of five parameters:
n = signal-to-noise ratio of the Nth principal component,
r2 = difference between the signal-to-noise ratio of principal components N and
N+1,
r3 = percent of average TS associated with the new source,
r4 = minimum percent of average TS of any source in the model, and
r5 = percent TS associated with the large new source contributions.
The signal-to-noise ratio of each component in the singular value decomposition
of the data is calculated by the NUMFACT algorithm (Henry, 1999). All else
being equal, the larger the value of r-\, the signal-to-noise ratio of the Nth principal
component, the better the model. Also, it is better to have a large difference
between the signal-to-noise ratio of components N and N+1 since this implies
that the information in the data (the signal) is concentrated in the first N principal
components. So larger values of r-\ and r2 are better, and the FOM should reflect
this.
The next three parts of the FOM are only defined if the data contains TS. For r3,
the percent of average TS associated with the new source, it is obviously better
that the new source added should explain as much of the total as possible. It is
also better if r4, the minimum percent of average TS of any source in the model,
be as large as possible since this tends to preclude having one or more sources
that explain very little mass. Finally, it is better when the newly added source
contribution is large (greater than 3 sigma) and that the percentage of TS
explained by the source is also large.
The FOM is calculated so that models that maximize the values of r-\ to r5 have
the largest FOM. Thus, if there are K models with N sources and rik is the value
of n for the Mh model, the evaluation number for the Mh source FOMk is
calculated as
where the weights w/, i = 1,...,5 are as follows:
M/ = (1 1 2 2 2) if TS explained by the new source is less than 5 percent and
i/i/ = (1 1 2 1 1) if the TS explained by the new sources is greater than 10 percent.
In between, the weights are linear. The terms in the denominator in the equation
for FOM are normalization factors that ensure that FOM is between 0 and 1.
Models are sorted by the FOM and the bigger the FOM, the better the model. If
33
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EPA Unmix 6.0 Fundamentals & User Guide
there is no TS in the data, then the FOM is calculated just as above, but the
weights of parts that depend on TS are set to 0 (w = (1 1 000) for all models).
The process of adding species one at a time to obtain models with ever-greater
number of sources continues until no new models are found. Uncertainties for
the source compositions of the final set of models are then calculated and
models with too much error are eliminated. If the data has TS, then models are
eliminated that have at least one source with TS less than 2 times the estimated
error. If there is no TS, models are eliminated if for at least one source the
source compositions are all less than twice the estimated error. Finally, a new
FOM is calculated for the remaining models. In this final calculation, the same
formula is used as given above, but r3 is replaced by the min r2 for the model and
the weights are (1121 2).
The parameters MaxParents, TSmin, SNMin, and MaxNumSolutions can be
changed. If a TS was selected, then TSmin is the minimum average percentage
of TS due to any source in a solution. The purpose of this is to prevent solutions
with sources that have very small contributions to the TS. As AU searches for
solutions, it uses each existing solution as a base from which to look for solutions
with one additional source. The number of existing solutions that will be followed
at each level is limited to MaxParents. If it is set to 5, for example, AU will only
follow the best 5 solutions at each level. The larger the value of MaxParents, the
more solutions Auto Unmix will find, but the run time will be increased.
MaxNumSolutions is the maximum number of solutions that Unmix will report.
SNMin is a highly technical parameter that controls the minimum signal-to-noise
ratio allowed in the solution. AU has three levels: Quick, Typical, and Deep. The
specific settings for each of the options are shown below.
Quick: MaxParents = 2, TSmin = 2, SNMin = 1.5, MaxNumSolutions = 2,
Unselected species r2 min = 0.5, feasible variability runs = 50, maximum number
of variability runs = 100;
Typical: MaxParents = 5, TSMin = 2, SNMin = 1.5, MaxNumSolutions = 5,
Unselected species r2 min = 0.3, feasible variability runs = 100, maximum
number of variability runs = 200;
Deep: MaxParents = 10, TSMin = 1, SNMin = 1.5, MaxNumSolutions = 10,
Unselected species r2 min = 0.3, feasible variability runs = 100, maximum
number of variability runs = 200.
This procedure can take from a few minutes to over an hour depending on the
AU settings and the number of unexcluded species, and automates the typical
steps that are used to develop the best possible Unmix solution based on the
data. An example of the AU algorithm is shown below using the wdcpmdata and
the Typical AU settings. Use the initial selected wdcmpdata species shown in
Figure 6 and select MF as the Total and Normalization (Norm) variable. On the
34
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EPA Unmix 6.0 Fundamentals & User Guide
right side of the Main window, select the Typical option for AU and select the AU
button as shown in Figure 20. Select "consider all species" to evaluate all of the
species in the Unselected Species box.
EPA Unmix 5.0
Select Anahce Selected Species Tools Help
Analyze Run I Highlight Run Output I Diagnostic Pints
Figure 22: Auto Unmix command
A window will open that shows the AU progress and the species that are being
evaluated (# shown next to species in Selected and Unselected Species boxes).
The analysis results from AU are displayed in Figure 21 and plotted in Figure 22
by selecting the Diagnostic Plots button, Variability Estimate (log) option, Figure
Groups button, and Number of Plots per page set to All. Two ten source solutions
were found with FOM values of 0.94 and 0.96. The FOM value is a relative
ranking and may not match these values due to the random number generator
used in the model. In addition, the number of solutions may not be the same due
to the randomized sequence of species selection. However, the best solution is
always displayed.
35
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EPA Unmix 6.0 Fundamentals & User Guide
> Analysis Results - EPA Unmix 6.0
"ools
Analysis Results
IAL o ooo"237 o 00-72 o 000165 o 00309 o DOSS? o°oi79 o°osi4 o Sosol o ooisz
B -0.00935 0.0912 0.0189 -0.0243 0.0889 0.286 0.00901 0.22 0.323
HH -1. 92e-QQ5 0. 000496 -7. 77e-006 0. 0003S8 Q.Q0020S 0. QQES1 0. 000172 0.000397 5. 28e-QQ5
03 0. 0383 0. 0303 D. 00742 -0. 0334 0. OE11 0. 000 934 O.QZSS -0. 059 0. 0604
S -0.00034 0.00492 0.00306 -0.0133 0.00535 0.0305 0.0935 0.0132 0.00531
£ 4 0.176 0.356 0.579 0.498 0.289 0.202 0.326 -0.3 0.156
FOH value Selected Species S
16-Hay-ZQ07 17:31:54
Tracer: Hone
TOTAL: HF
Normalisation: HF
Hin Rsq = 0.98, Hin Sig/Hoise= 1.52
AL -0. 000116 0. 00457 D.OOZ63 0. 000271 0. 00093 0.0 151 0. 00741 0. 0493 0. 000909
EC -0.00876 0.0821 0.0563 0.0233 -4.88e-Q05 0.244 0-1 0.0159 0.328
HH -1. 82e-Q05 0. 000482 -0. 000575 2. 43e-QQE 0.000431 0. 00428 0. 000183 0.000261 0. 000113
PE 0. 000103 0. 000 551 0.00967 2. 16e-00£ 0.0 001 24 0. 000212 0. 00012 3. 06e-OOE 0.000345
SE 3.64e-005 0-00011S -3. 03e-005 2_18e-QOS 5.63e-Q05 0.000312 0,00136 3.67e-QQ6 4.39e-Q05
SI 0. 000109 0.0102 -0.00284 0.00331 -0.00286 0.0218 0.00596 0.0891 O.OOS1
V -7. 84e-QQ6 -0.000447 -0. 000432 6. 71e-QQE 0. 00705 0. 00148 0. 000611 0. 000104 -8. 97e-00£
ELAPSED TIME = 0 MINUTES 27.0 SECONDS
0.00987
-4.S9e-QQ£
0.319
0.00113
0.0343
2.04
0.00113
0.0501
2.19e-005
O.S81
0.2
5.36e-005
8.37e-005
0.000841
0.000208
^^^nti^^
•^^H
Ell®
v 1
-^
Figure 23: AU result for wdcpmdata
36
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EPA Unmix 6.0 Fundamentals & User Guide
Figure Groups - EPA Unmix 6.0
File Save As
Figure GrOUp:|Error Estimate
Source #1 Soul
T I Number of plots per page
Source #4
Figure 24: AU Source Profiles
The species from the highest FOM are loaded into the Selected Species box.
Evaluate the AU solution in more detail by selecting the Analyze Run and
Diagnostic Plots buttons. The Fit Additional Species command can be used to
find species (i.e. species with R2 greater than 0.80) that can be added to the AU
solution. Evaluate any final solutions with the Diagnostic Plots ^ Fit Diagnostics
and Analyze Run ^ Variability Distribution commands.
A warning message that "No additional species found" will be displayed if AU
cannot find any additional solutions. Try removing some of the species in the
Selected Species box or do not use a TS. Another option is to try running AU
with the Deep setting.
SECTION 5. ADVANCED OPERATIONS
The basic strength of Unmix, as with all receptor models, is that it relies on the
data; the basic weakness of Unmix is that it relies on the data. A number of
problems may afflict a species and make it unsuitable for selection to be part of
the model. A common problem is that the species may have missing
37
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EPA Unmix 6.0 Fundamentals & User Guide
concentration data, however, the Replace Missing Values (see Section 5.5)
command in Unmix can be used to replace missing data. Another common
problem is the existence of outliers in the values of the species. These can often
be detected using scatterplots as described in the section on View/Edit
Observations & Points, or by using the Influential Points command (see Section
5.2). Sometimes a species may have a lot of noise associated with it.
Measurement error is one source of noise, especially when the species is just
above the minimum detectable limit. Finally, a species may not be suitable
because it violates the assumption inherent in all receptor models that the source
compositions are approximately constant. If the mass fraction of a species varies
enough, it will destroy the constraints in the data that Unmix uses to obtain a
solution. Lewis et a/. (1998) discusses some possible data problems and how to
identify these.
5.1 Influential Observations
The tools for evaluating influential observations and points are listed in the lower
left corner of the Data Processing window under View/Edit Points and
Observations. Select the View/Edit Points and Observations list on the Data
Processing window, after removing the wdcpmdata species that were
recommended for exclusion in Figure 5. Select the View/Edit Observations &
Points command and consider all species as seen in Figure 23. Select MF as
the base species.
38
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Data Processing - EPA Unmix 6.0
File Specie? Paints and Observations About
_J Do not replace or use highlighted species
Figure 25: View/Edit Observations & Points
All of the species concentrations are plotted against the selected base species
and the edges are displayed with dashed red lines (Figure 24). The size of the
figures can be increased by reducing the number of species or by selecting a
figure and the Undock button. Observations or data points contributing to the
poor upper edges can be deleted in the Species vs. Base Figure by selecting the
point in the figure with the left mouse button. For example, go to the OC1 figure
(4th column, 3rd row) and choose the high OC1 point by placing the tip of the
arrow near the point, holding down the left mouse key and increasing the size of
the selection box until it contains the point. Release the left mouse key and the
point will be identified with a red square and the other species for that sample will
be circled in the other plots. Multiple points can also be selected in a plot by
choosing a location near one of the points in the plot (not outside of the plot),
holding down the left mouse key, increasing the size of the box until the points
are within the box, and releasing the mouse key.
39
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EPA Unmix 6.0 Fundamentals & User Guide
.' View/Edit Observations ft Points - EPA Unmix 6.0
File Edit Data Font
Base Species: MF
0 50
MF
Figure 26: View/Edit Observations & Points plot high OC1 point
Select the Edit Data ^ Delete Selected Observation(s) command from the top
left of the View/Edit Observations & Points window. After all of the species
related to the deleted observation are removed, new edges are drawn (as
displayed in Figure 25) and the observation number of the deleted point is
recorded in the Data Processing Report. If a figure is too small to select an
individual point, reduce the number of highlighted species before selecting the
View/Edit Observations & Points command. Another option if the figure is small
is to select a figure and then select the Undock button. This will create a window
with only the selected figure. Undocked figures cannot be used for selecting
observations. The data points can be restored in the Edit Data command using
the Restore Most Recently Added or Restore All options.
40
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EPA Unmix 6.0 Fundamentals & User Guide
0 50
MF
Figure 27: New edges in View/Edit Observations & Points plot
Select the Save Changes and Close buttons on the View/Edit Observations &
Points window. Select the Data Processing Report button in the upper right
corner of the Data Processing window to view the report, or export the report
from the Analyze and Export Run Results window, Data Processing Report
option. An example report is shown in the following Figure 26. The sample
collected on 04/08/1992 was deleted and the OC1 value was 5.46.
41
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EPA Unmix 6.0 Fundamentals & User Guide
Data Processing Report EPA Unmix 6.0
Data Processing Report - EPA Unmix 6.0
Removed
Observations : 303
Influential Points
Species
HF
AL
A3
ER
CA
CU
EC
EC1
FE
K
HN
HI
N0:i
OC
OC1
Date
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/S/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
4/8/1992
Information:
Old
29.6000
0.1052
D.D032
0.0046
0.0918
0.0047
2.6700
3 . 1200
0.1850
0.0832
0.0057
0.0032
1.2800
10.9000
5.4600
Hew
HaH
HaH
NaN
NaH
NaN
NaN
HaH
NaN
NaH
NaH
HaH
NaH
nan
NaN
NaN
Change
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Deleted
Type
Obs.
Obs.
Otas.
Obs.
Obs.
Obs.
Otas.
Obs.
Obs.
Obs.
Obs.
Otas.
Obs.
Obs.
Obs. v
Figure 28: Data Processing Report
A point can be identified in the View/Edit Observations & Points plot by selecting
the Edit Data ^ Datacursor Mode command. For example, select the high K
value in the K vs. MF plot. Figure 27 shows that the high K value was on
07/05/2000 and was most likely impacted by 4th of July fireworks. This individual
point can be removed using the Edit Data ^ Delete Selected Point(s) command.
The selected non-base species point in the observation is replaced with a
missing value symbol and the other species concentrations in the observation
remain unchanged. The Replace Missing Value command can be used to
replace the deleted point with a value that is consistent with the other species
concentrations in the observation.
42
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EPA Unmix 6.0 Fundamentals & User Guide
.' View/Edit Observations ft Points - EPA Unmix 6.0
File Edit Data Font
Base Species: MF
Figure 29: Datacursor Mode
The Datacursor Mode command is turned off by re-selecting the Edit Data ^
Datacursor Mode command. After the Datacursor mode is turned off, the figures
are re-drawn resulting in a delay in the window commands being available. Save
the modified data set by selecting Save Changes. It should be noted that Unmix
saves the deleted point information in the Run Profile (see Section 3.9).
5.2 Influential Points
The View/Edit Influential Points command identifies those points that influence
the definition of an edge significantly. A point is considered to be highly
influential, if after removal of the point, the edge moves significantly. Influential
points can significantly affect the nature of the solution produced by the SAFER
algorithm for a chosen group of species. That is, the SAFER algorithm that failed
to produce a feasible solution for a chosen set of species can produce a feasible
solution for the same set of species after deleting just one observation deemed
highly influential from one of the chosen species. The View/Edit Influential Points
command can be used to remove a single point which then can be replaced
using the Replace Missing Value command.
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EPA Unmix 6.0 Fundamentals & User Guide
Influential points are identified using three parameters: P, alpha, and K. P is the
fraction of the total number of points near the edge that are used in the statistical
modeling of the edge. The value for P is 0.25, and if there are N points, the
algorithm only looks at the 25 percent closest to the edge; there are n1 = P*N of
these. An adjustable parameter alpha is related to determining influential points.
Before discussing alpha, the working of the algorithm must be explained. The
following discusses in detail how the influential points algorithm works.
The axes of the data are rotated to align with the edge. Thus, each data point's
perpendicular distance from the edge becomes its y-coordinate (dy1) and the x-
coordinate is distance along the edge (dx1). The algorithm looks for points with
unusually large negative values of dy1 (points below the edge) and points with
unusually large distances along the edge as given by dx1.
Since most air quality data are approximately lognormally distributed, dx1 is
assumed to be lognormally distributed. Next, the values of dx1 are converted to
a standard normal distribution by taking logs and subtracting the mean and
dividing by the standard deviation. The parameter alpha takes values from 0 to
1: alpha = 1 corresponds to allowing 1 outlier in the sample of n1 points near the
edge, and alpha = 0.5 corresponds to allowing 0.5 outliers (on average). The
smaller the alpha, the fewer points are flagged as possible influential points.
Thus, the alpha or longitudinal spread ranges from 0 to 0.35 with a default value
of 0.05, with the larger values flaging more points as influential.
Most points are flagged as influential because they lie too far below the edge
(dy1 values are large and negative). Because of random noise in the data, some
of the points will be below the edge. Assume a uniform distribution of points near
the edge with simple Gaussian noise, it can be shown that the squared distance
of the point from the edge divided by the sum of the squared distances from the
edge should be less than a multiple of 3/n1. This multiple is defined as K or the
transverse spread which ranges from 2 to 15, with a default of 10. In this case,
the smaller values of K would flag more points as influential.
In addition to identifying influential points these plots also display the "Max.
Common Source Contribution." One can get some additional information from
the lower edge in a plot of a species (V) versus a species (T). Assume V has
more than one source and that the source with the largest fraction of V is source
S. The inverse of the slope of the edge is an estimate of the fraction of V in
source S. Furthermore, the slope times the mean of V divided by the mean of T
is an estimate of the maximum fraction of average T contributed by source S.
This information can be useful in helping to decide if the influential points that
have been identified by the algorithm should be eliminated or not. Also, this kind
of information can be helpful in deciding if a small source associated with a single
species found by Unmix is physically reasonable.
44
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EPA Unmix 6.0 Fundamentals & User Guide
The edge resolution number is useful in characterizing the edge definition. The
value 0 suggests an unresolved edge and 1 a perfectly resolved edge. The
intermediate values accurately indicates how "good" the edge is. The edge
resolution number displayed pertains to the edge defined by the red dashed line
(prior to removing the influential points). This is likely to improve when the
suggested influential points are removed.
Load the STN_PM.xls data set from the C:\Program Files\EPA Unmix 6.0\Data
folder. This is an example particulate matter data set from a Speciation Trends
Network (STN) site. The data file contains dates in the first column and the
missing value symbol is -99 (Figure 28).
EPA Unmix 6.0
File Select Analyze Selected Species Tools Help
Analyze Run I Highlight Run Output I Diagnostic Plots
Figure 30: Example STN PM data set
Select the Suggest Exclusion button ^ and then exclude the suggested species
by selecting the Exclude button. A large number of the trace elemental species
are recommended for exclusion (Figure 29).
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Data Processing - EPA Unmix 6.0
File Specie? Paints and Observations About
Process Input Data
C:\Program Res'CPA Unmix 6. O
I Included Species
I Name
Fine
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View/Edit Points and
Observations
Do not replace or use highlighted species
Replace Missing Values
Suggest Exclusion
Restore Original Data
Data Processing Report
Help
ant-hanum
iobiuni
^osphorus
: andium
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ilver
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Figure 31: Example STN PM excluded species
Select the View/Edit Points and Observations list at the bottom left corner of the
window and select the View/Edit Influential Points command. Use the default
longitudinal and transverse spread parameters (Figure 30). All of the influential
points can also be deleted without viewing the plots by selecting the Remove
Influential Points option in the View/Edit Points and Observations list.
46
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EPA Unmix 6.0 Fundamentals & User Guide
FPA Unmix 6.0
Process Input Data
Data Processing Report
Input F
^^^^
Included Species
Nan*;
Do you wish to find the influential points for all combinations (380)?
If the number of combinations are too many, press "Cancel" first.
Highlight desired species in the "Included Species" box
before requesting influential points.
View/Edit Points and
Observations
_J Do not replace or use highlighted species
Save Input Data
™^
Cancel OK
Replace Missing Values
Figure 32: Influential Points command
Select the All button to find the influential points for all combinations of the
selected species. In the scatter plot (Figure 31), the red circled points are the
influential points. The red dashed line is the edge defined by the data values
when none of the influential points are removed. The black solid line is the mean
edge after removing all of the influential points and the black dashed lines below
and above the black solid lines are the lower and upper estimates of the edges
after the influential points have been removed. Use the Next and Previous
buttons to view the species combinations with influential points. The influential
point information is also listed in the Data Processing Report. Use the Next
button to select the 3rd figure, the Potassium vs. Zinc plot.
47
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EPA Unmix 6.0 Fundamentals & User Guide
Max. Common Source Contribution I! % FHqp resolution n ."'4
Figure 33: Influential potassium point
Highlight observation 157 in the Influential Observation list and the date of the
sample and longitudinal distance will be displayed on the plot (Figure 32).
48
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EPA Unmix 6.0 Fundamentals & User Guide
Max. Common Source Contribution I! % FHqp resolution n ."'4
1L18 |L [list!
Figure 34: Influential points
The high potassium concentration is from a sample collected on the 4th of July
(fireworks). Select the Exclude button to move the observation number to the
Deleted Influential Observation list. Select the Update Figure button to view the
figure without the influential point. The edge resolution improves after removing
the point by increasing from 0.24 to 0.84.
The spread parameters in the Influential Points window can be changed by
changing the longitudinal spread or transverse spread parameters and selecting
the Update Figure button. Increasing the longitudinal spread to 0.08 captured
three additional high Potassium points. The high Potassium points can be
deleted using the updated list of influential points or View/Edit Observations &
Points command, Edit Data ^ Delete Selected Point(s) command. Use the
Replace Missing Values command to replace the deleted values.
5.3 Apportionment of Species Not in the Model
Once Unmix has found a solution, the user may be interested in how well the rest
of the species in the data are fit by the sources in the solution. The unselected
species are evaluated by selecting the Species Selection Tools, Fit Unselected
49
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EPA Unmix 6.0 Fundamentals & User Guide
Species command (Figure 33). Figure 34 shows the results for the wdcpmdata
species (Refer to Figure 11).
EPA Unmix 6.0
Select Analyze Selected Species Tools
I- II* X'
• Analyze Run I Highlight Run Output I Diagnostic Plots
Figure 35: Fit Unselected Species command
50
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EPA Unmix 6.0 Fundamentals & User Guide
.' Analysis Results - EPA Unmix 6.0 1 - II H | X |
Tools
Analysis Results
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Figure 36: Fit Unselected Species Results
Each row is the result of a non-negative least squares regression of the source
contributions (normalized to a mean of 1) and the species. The amount of the
species in each of the sources, the amount not explained by the sources or
constant, and coefficient of determination are displayed. Results are also sorted
by the species R2.
These results can also help guide the selection of additional species that can be
added to the Unmix solution. For example, OC2 has a high R2 value and after
adding it to the Selected Species Window and selecting the Run button, the
solution in Figure 35 is produced. This command can be used to create a
consistent set of species for comparing EPA Unmix and EPA PMF profiles.
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EPA Unmix 6.0 Fundamentals & User Guide
.' Analysis Results - EPA Unmix 6.0 1 - II H | X |
Tools
Analysis Results
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Figure 37: Adding species from Fit Unselected Species
5.4 Factor Analysis
The Unmix results can be compared to the typical factor analysis approach
(varimax rotated factor analysis) by selecting the Species Selection Tools, Factor
Analyze Selections command. Use the Factor Analyze Selections command to
evaluate the Unmix results shown in Figure 36.
52
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Select AnaKoi- Selected species Tools
Figure 38: Factor Analyze Selections command
The factor, matrix scores, covariance matrix scores, explained covariance, and
Scree plot are displayed. Select the Display Loadings button to show the
loadings. The number of factors can be changed by selecting a value in the
Number of Factors list. Selecting the Display Loadings button again will show
the loadings associated with the new number of factors (Figure 37).
53
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EPA Unmix 6.0 Fundamentals & User Guide
Figure 39: Factor Analysis Results
Four factors have Eigenvalues greater than 1, which has been used as a cutoff
for determining the number of factors in air pollution data. Compared to the
factor analysis, Unmix is extracting three additional factors from the data. The
factor analysis results can also be compared to the strong and significant species
listed in the Fit Diagnostics output. Factor 1 represents motor vehicles with high
species loadings on EC, EC1, N03, OC, OC3, and OC4. Factor 2 represents
crustal material with high factor loadings on Al and Si. Factor 3 represents wood
burning with high loadings on K and SolK. Factor 4 represents secondary sulfate
and additional combustion aerosol with high loadings on EC, EC1, OC2, and
S04.
5.5 Replace Missing Data
One common question when applying Unmix is what to do with species that have
many missing values. Unmix does not use data from a sample if even one of the
selected species has a missing value. For most species with many missing
values, the solution is simply not to include these species in the model.
However, sometimes the species are important because they could be indicators
of a source. Selenium, nickel, and vanadium are examples of elements that
often have many values below minimum detectable limits or infrequent point
54
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EPA Unmix 6.0 Fundamentals & User Guide
source impacts, but when these have high values, it may signify the impact of
important sources such as coal combustion and residual oil combustion.
In general, missing values result from two causes. First is mechanical failure of
the sampler, loss of the sample or other irretrievable event. Nothing can be done
in these cases. Second and more often, missing data are below the minimum
quantifiable (or detectable) limit. Data may be too low to quantify for two
reasons: the amount in the sample is very low, or the amount in the sample is not
small, but the species detection limit is raised by the presence of a large, near-
by, interfering species.
Unmix allows the option of replacing missing values. Table 3 illustrates how a
missing value is estimated. The fundamental idea is to find a value that is
consistent with the ratios of the species in the data. In this example, 200 of the
400 values of VOC3 less than 100 in the umtest.txt data set were assumed to be
missing. The method of finding a number to fill in a missing value is illustrated
using row 15 of the umtestR.txt data. These data are reproduced as the first
column in the table. The next column gives the smallest ratio of VOC3, when it is
not missing, divided by each remaining VOC. The maximum ratio is in the next
column.
To understand the algorithm, first consider VOC1. It has a concentration in the
sample of 1.86, and when this is multiplied by the min and max ratios we get the
concentrations 1.99 and 145.74 in the last two columns. The first is the smallest
concentration of VOC3 that would be consistent with the observed ratios with
VOC1 in the data. If VOC3 were smaller than this value, the ratio with VOC1
would be smaller than anything seen in the rest of the data. Similarly, if VOC3 is
greater than 145.74, this would be outside the range of ratios with VOC1 seen in
the data. Now VOC3 could have a value anywhere between 1.99 and 145.74
and be consistent with the rest of the VOC1 data.
The same calculation of limits is made for each VOC and Total. Notice that the
smallest value of VOC3 that is consistent with all the data is the maximum of the
minimum values for each species, which is 5.99. By the same reasoning, the
largest value of VOC3 that is consistent with the data is the minimum of the
maximum values given in the Table, or 15.67. This puts a fairly tight range of
5.99 to 15.67 on the possible values for the missing VOC3 concentration. The
simple arithmetic mean might be chosen as the best estimate of the missing
value. This is true if the distribution of the values is symmetric around the mean.
However, air quality data is usually not so distributed, most often following a
skewed distribution such as a lognormal orweibull distribution. In this case, the
geometric mean is a better estimate of the most likely value. Thus, the final
estimate of the missing VOC3 value is the geometric mean of 5.99 and 15.67, or
9.69. This compares well to the value of 11.83 in the original data. Finally, it is
possible for the estimated minimum value to be greater than the estimated
maximum value; if this happens the missing value is not replaced.
55
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EPA Unmix 6.0 Fundamentals & User Guide
Table 3: Missing Value Estimation
Concentration Min. Ratio Max. Ratio Min. Cone. Max. Cone.
to VOC 3 to VOC3 from ratios from ratios
VOC1 1.86 1.07 78.36 1.99 145.74
VOC2 8.84 0.68 1.91 5.99 16.88
VOC3 * * * * *
VOC4 3.40 0.77 8.29 2.61 28.19
VOC5 1.13 2.49 15.65 2.81 17.69
VOC6 3.61 0.92 5.53 3.33 19.97
VOC7 3.60 0.98 6.99 3.53 25.17
VOC8 3.47 0.84 8.71 2.92 30.22
VOC9 4.03 1.18 5.29 4.77 21.30
Total 61.92 0.09 0.25 5.64 15.67
Max of the minimums 5.99
Min of the maximums 15.67
Geometric mean 9.69 Value used to replace missing value
Original 11.83
concentration
This method of filling in missing values has some obvious limitations. For the
missing values of a species to be properly estimated, the species cannot be
missing all or almost all of the time. If the species has almost all of its values
missing, then the ratios of the non-missing data to the other species will not be
representative and the estimates will be unreliable. Also, the greater number of
species in the data, the better the method will work. Of course, one must always
be cautious in replacing missing data. A basic assumption is that the conditions
and contributing sources during the periods of missing data are the same as for
the rest of the data. If for some reason this is not the case, then filling in missing
data based on the existing data may not be advisable. Experience has shown
that this method of dealing with missing data does not degrade Unmix solutions.
In some cases, species cannot be replaced when the minimum replacement
value is at least 1% greater than the maximum replacement value.
As a broad guideline, a species should have no more than about two-thirds
missing data, but this depends on how many data points there are in the whole
data set. Fewer points would require less missing data. Be sure to select all the
species that have mostly non-missing data. It is these species that will be used
by the algorithm to estimate the species with many missing values. It is not
recommended at this time to mix data of different types (particulate data and gas
data). Missing total data should not be replaced. Data files with and without
missing data (umtest.txt) and with missing data (umtestR.txt) are included with
EPA Unmix in the data folder. The umtestR data are the same as the umtest,
except that VOC species 2 and 6 have some missing data. Load the umtestR
data. The data do not have any date or time information and the missing value
symbol is -99. In the Data Processing window, highlight the TOTAL variable in
the Included Species box and select the Do not replace or use highlighted
species checkbox. Next, select the Replace Missing Values button (Figure 38).
56
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EPA Unmix 6.0 Fundamentals & User Guide
Input Filename : | C:^Program Filer'CPA Untm,. 6 DIDaiaiiuraiestK T;- r
^^^^^^^^^^K
Included Species
Figure 40: Replace Missing Values command
The number of replaced values and the replaced mean (RM) are displayed. The
modified input data file can be saved for use by other programs using the Save
Input Data button. The replaced values are reported in the Data Processing
Report (Figure 39).
57
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EPA Unmix 6.0 Fundamentals & User Guide
Data Processing Report EPA Unmix 6.0
Data Processing Report - EPA Unmix 6.0
ssing Data Replacement Requested: Yes
•Hissing data not replaced for the following:
ITOTAL
Species 8 Obs
VOC2 1
5
6
10
11
IB
21
22
25
29
41
12
55
58
61
69
73
79
89
99
107
108
111
115
123
126
127
136
137
142
143
Old
Mail
Mail
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Hall
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HaH
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36.2152
22.1647
44.2177
21.7103
26.4779
29.2044
44.7403
5.4206
23.4433
2B.8144
16.4076
32.5590
20.5417
15.1610
23 .9747
16.0160
33.9830
5.3511
33.5837
20. 6357
27. 1797
15.7604
13.6916
24.9826
25.4641
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18.4660
IB. 4134
23.5519
19.0108
29.0389
Hew Change Type
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ed Ob 3
Page 57 Sec 2
Figure 41: Replaced missing values
Close the Data Processing Report and select the OK button in the Data
Processing window. Move all of the species to the Selected Species box. Set
VOC1 as a Tracer, Total as the Total and Norm variable, and select the Run
Type I option and Run button. Unmix results from using the original umtest data
and after replacing the data in umtestR are shown in Figure 40.
58
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EPA Unmix 6.0 Fundamentals & User Guide
Analysis Results EPA Unmix 6.0
Analysis Results
Tracer: VOC1
10 Species, 400 Obs., 3
•lin Esq = 0.99, Hin Si
VOC1
VQC2
70C3
0.111 0.148 0.143
0.107 Q.Q99S 0.226
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Tracer: VOC1
Unmix
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0.Ill 0 4.9Se-01S
0-111 0.147 0.144
0.11 0.1 0.223
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;LAPSED TIHE = o HIHUTES 0.4 SECQHDS
Figure 42: Comparison of umtestR and umtest results
SECTION 6. ADVANCE PLOTTING OPTIONS
EPA Unmix can be used to create custom figures that can be printed and
exported for use in other programs. All plots can be saved by selecting File and
the Save command (Figure 41).
59
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EPA Unmix 6.0 Fundamentals & User Guide
Diagnostic Plots - EPA Unmix 6.0
Undock Figure • Figure Groups
Source composiiions tor run #2 - Linear Scale
0 Source Composition
| I Source Contribution
Source Composition
n Signal-To-Hoise
[J Confidence Internal
G Variability
O Variability Distribution
Edge Plot (Source Contribution)
Base Source:
! I Fit Diagnostics
G Standardized Residuals
Figure 43: Saving Diagnostic Plots
6.1 Figure Groups
The following figures can be created using the results from the analysis of the
wdcpmdata species from Run # 2 in Figure 11. Select the Diagnostics Plots
button from the main window and select Source Composition (Log), Source
Contribution (Actual), and Fit Diagnostic options. The source profiles (in mass
fraction) will be displayed with two profiles on each chart (Figure 42).
60
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EPA Unmix 6.0 Fundamentals & User Guide
Diagnostic Plots EPA Unmix 6.0
Undock Figure II Figure Groups
Diagnostic Plots for Run Number 2
Source composil ons for run #2 - Log Scale.
Plot Options
0 Source Composition
O Linear 0 Log
0 Source Contribution
O Normalized
O Uniform
© Actual
Evaluation
Source Composition
Q Signal- To Hoise
O Confidence Interval
G Variability
G Variability Distribution
G Edge Plot (Source Contribut on)
Base Source :
Species
0 Fit Diagnostics
G Standardized Residuals
Figure 44: Source profile plots
Select the Figure Groups button and set the number of plots per page to All. A
new figure will be created that contains all of the source profiles (Figure 45).
Select the Figure Groups list to view the groups: Source Composition, Source
Contribution, Fit Diagnostics - Scatter Plot, and Fit Diagnostics - Time Series.
61
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EPA Unmix 6.0 Fundamentals & User Guide
> Figure Groups - EPA Unmix 6.0
Fiie Save As
Figure Group:
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6.2 Edge Plots
A basic explanation of how Unmix uses edges in the data is found in Henry,
1997. An example of the edge plots is shown below using the umpmdata.txt file
located in the C:\Program Files\EPA Unmix 6.0\Data directory. Load the
umpmdata data (no date or hour information, missing value symbol is -99).
Exclude the gases (N02 and CO) and exclude the suggested species that are
recommended for exclusion (As, Sr) and select the OK button.
Move MASS, Al, Si, S, K, Fe, OC, EC, and Sol_K (soil corrected K) from the
Unselected to Selected Species window. Set MASS as the Total and Norm
species and select the Run button (Figure 44). These selected species give a
four source model.
62
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EPA Unmix 6.0 Fundamentals & User Guide
EPA Unmix 6.0
Select Anako; Selected Species Tools Help
Figure 46: Umpdata edge plot example
To generate a plot of the source profiles, select the Diagnostic Plots button,
Source Composition (linear) option, and Generate Plots button. Select the
Figure Groups button to display the profiles on one plot. The four sources are
vegetative or wood smoke (source 1), secondary sulfate (source 2), motor
vehicle (source 3), and crustal (source 4) as seen in Figure 45.
63
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EPA Unmix 6.0 Fundamentals & User Guide
Figure Groups - EPA Unmix 6.0
File Save As
Figure Group: Source Composition
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EPA Unmix 6.0 Fundamentals & User Guide
Diagnostic Plots EPA Unmix 6.0
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FJ Source Composition
fj Source Contribution
Evaluation
Source Composition
fj Signal- To Hoise
Q Confidence Interval
G Variability
G Variability Distribution
[7] Edge Plot (Source Contribut on)
Base Source : 2 -"I
Species
G Fit Diagnostics
G Standardized Residuals
Generate Plots
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Figure 48: Edge Plots
The numbers plotted are the fraction of the sample that is from each source, thus
the numbers lie between 0 and 1, except for the effects of error. The x and y
axes are the edges. In both plots, the y-axis is the edge associated with source
2, the secondary sulfate. Points that are near the y-axis have very small
contributions from vegetative or wood smoke source (source 1). All the edges in
these plots are typical of "good" edges. Points can be selected by holding the left
mouse button down and drawing a rectangle around them. Select the points with
low motor vehicle contributions (Source 3). The selected points are contained
within red squares while red circles are drawn around the same samples in the
other figures (Figure 47).
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EPA Unmix 6.0 Fundamentals & User Guide
Diagnostic Plots - EPA Unmix 6.0
Diagnostic Plots for Run Number 1
Source 2
Plot Options
Source Compositio
] Source Contribution
Evaluation
Source Composition
Q Signal To Hoise
Q Confidence Interval
O Variability
G Variability Distribution
[7] Edge Plot (Source Contribut on)
Base Source : 2 -1
Species
O Fit Diagnostics
G Standardized Residuals
Figure 49: Selected Points in Edge Plots
The observation numbers are also displayed in the Analysis Results window. An
example of poor edges can be seen by adding Zn to the species and running
Unmix again. Evaluate the new five source solution by re-plotting the edge plots
against the secondary sulfate source (source 3). Select the points near the x-
axis in the source 4 plot (Figure 48).
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EPA Unmix 6.0 Fundamentals & User Guide
Diagnostic Plots EPA Unmix 6.0
Undock Figure II Figure Groups
Diagnostic Plots for Run Number 2
Source 3
G Fit Diagnostics
G Standardized Residuals
Plot Options
G Source Composition
G Source Contribution
Evaluation
Source Composition
G Signal-To Hoise
G Confidence Interval
G Variability
G Variability Distribution
[7] Edge Plot (Source Contribution)
Base Source : 3 71
Figure 50: Example of poorly defined edges
The source 4 plot has just a few points near the x-axis that define the edge. In
general, edges that are dependent on just a few points will be more greatly
affected by errors than edges that are defined by many points. Since Unmix
uses edges to find the source compositions, poor edges will lead to increased
variability in the source compositions.
SECTION 7. BATCH MODE
The Batch Mode command can be used to evaluate the addition of species
recommended by the Suggest Additional Species command. Batch mode will
add all combinations of the highlighted species in the Unselected Species
window to the Selected Species and evaluate each set of species. To run the
Batch Mode command, select the Batch mode radio button and select the Run
button. The following example uses the wdcpmdata data file and the selected
wdcpmdata species from Run # 2 in Figure 11. Run the Influential Point
Algorithm to obtain information on the species that have not been highlighted in
the Unselected Species box (Figure 49).
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EPA Unmix 6.0 Fundamentals & User Guide
Analyze selected species Tools Help
Unselected Species
Selected Species
Hobs
Input Data Processing
Species Selection Tools
lalyze Selected Species
Would you like to use influential point.; algorithm and obtain batch mode
specie; E.elechnn suggestion?
* Sources: Min: 3 Max: 7
% Sources lor the Current Run:
m
Run Type :: Individual CO Batch
Analysis Diagnostics
Quick Typical O Deep
Run # * Species # Obs # Sources Min. Win. Run
Rsq SigJNoise Type
Figure 51: Batch mode influential point option
Select species with good edge resolution and low number of influential points
from the Species Suggestions Window. For this example, select Zn, Ti, Fe, Ca,
OC2, Pb, and Se. Choose the Select button and the Batch Mode Preferences
window will open (Figure 50). Save the Batch mode results in a data file and
select the OK button.
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EPA Unmix 6.0 Fundamentals & User Guide
Figure 52: Batch Mode Preferences
Progress bars will show the Batch mode status. The Batch mode can be
stopped by selecting the Stop Run button and the results will be saved in the
output file. The Solution Summary box will list the Batch Mode results (Run Type
"B") as shown in Figure 51. The Analyze Run and Diagnostic Plots buttons are
not available for Batch Mode model results.
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EPA Unmix 6.0
Select AnaKoi- Selected species Tools
Figure 53: Batch Mode Solution Summary
Choose Run # 121 from the Solution Summary and select the Highlight Run
Output button to view the results (Figure 51). The run number may be different
due to the number of individual runs prior to the batch mode run but will have 18
species and be before the "NO FEASIBLE OR PARTIAL SOLUTION" and before
the # Species increases to 19. Five species were added to the selected species:
OC2, PB, SE, Tl, and ZN (Figure 52).
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Batch Run Output EPA Unmix 6.0
Batch Run Output - EPA Unmix 6.0
•Variable(s) added: OC2
PB
|31-Jan-2QQ7 17:19:01
Irile: C:\Prograin Files\EPA Unmix 6 . 0\ Data\ wclcprndata.
|Tracer: None
TOTAL: MF
Horinal i sat ion: MF
Species, 1171 Obs., 7 Sources,
Illin Rsq = 0.87, Hin Sicf/Noise= 2.06
Species
HF
AL
EC
EC1
K
NO3
OC
OC2
OC3
OC4
501K
PB
SE
31
SOI
TI
V
ZM
Source 1
2 -SI
0.000362
0.00877
-0.00612
0.00176
0. 453
0.161
0.0126
0.0663
0.0752
0.00184
0.000233
0.000196
-0.000729
0.194
0.000292
0.000114
0.00121
Source 2 Source
r 0.163,
0.0133,
-0.0251,
0.0162,
, 0.195,
, 0.0574,
0.326,
0.0495,
, 0.124,
0.0863,
, 0.196,
0.00454, 9.
, -9.01e-005, 3
-0.00432,
, 0.216,
, 0.00308,
0.0003B2, 0
, 7.29e-005, 0
3 Source
1.32,
0.033,
0.0311,
0.0321,
0.00646,
0.0194,
0.118,
0.0311,
0.0294,
0.0317,
0.00039,
68e-005,
.6e-005,
0.0606,
0.358,
0.00231,
.000139,
.000407,
4 Source
0.471,
0.0105,
0.204,
0.107,
0.0118,
0.0248,
0.313,
0.00376,
0.157,
0.162,
0.0113,
0.00219,
0.00103,
0.00595,
-0.126,
0.00325,
0.008S7,
0.00808,
5 Source
7.46,
0.0012,
0.0317,
0.0337,
0.000684,
0.00902,
0.0993,
0.0314,
0.0204,
0.0319,
0.000319,
0.000104,
0.000118,
0.00363,
0.514,
0.000658,
0.000102,
0.000245,
6 Source
0.727,
0.00105,
0.59B,
0.791,
0.000349,
0. 152,
-0.279,
0.0165,
-0.32,
-0.254,
-0.00164,
0.00564,
-0.000394,
0.0194,
0.522,
-0.00288,
-0.00123,
0.006,
7
3 .7
0.00082
0.129
0.145
0.00302
0.0339
0.438
0.0755
0.165
0.127
0.00287
-0.000312
0.000123
0.0014
0.0818
0.000392
0.000304
0.000502
•ELAPSED TIME = o HIHUTES s.4 SECONDS
Figure 54: Batch Mode Analysis Results
Select the Load Species button to add these species to the Selected Species box
and select the Run button. The new solution can now be evaluated with the
Analyze Run and Diagnostic Plots options.
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EPA Unmix 6.0 Fundamentals & User Guide
SECTION 8. Unmix PUBLICATIONS
Henry R.C. (2005) Duality in multivariate receptor models. Chemometrics and
intelligent laboratory systems. 77: 59 - 63.
Henry R.C. (2003) Multivariate receptor modeling by N-dimensional edge
detection. Chemometrics and intelligent laboratory systems. 65: 179- 189.
Henry R.C. (2002) Multivariate receptor models- current practices and
future trends. Chemometrics and intelligent laboratory systems 60: 43- 48.
Eun Sug. Park, C. Spiegelman, and R.C. Henry (2000) Estimating the number of
factors to include in a high-dimensional multivariate bilinear model.
Communications in Statistics, Simulation & Computation 29: 723-746.
Henry, R.C. and B.- M. Kim (1989) A Factor Analysis Model with Explicit Physical
Constraints, Transactions Air Pollut. Control Assoc. 14:214-225.
Henry, R.C. and B.-M. Kim (1990) Extension of Self-Modeling Curve Resolution
to Mixtures of More Than Three Components. Part 1: Finding the Basic Feasible
Region, Chemom. Intell. Lab. Syst. 8:205-216.
Henry, R.C., C.W. Lewis, and J.F. Collins (1994) Vehicle-Related Hydrocarbon
Source Composition from Ambient Data: The GRACE/SAFER Method, Environ.
Sci. Technol. 28:823-832.
Henry, R.C. (1997) History and Fundamentals of Multivariate Air Quality
Receptor Models, Chemom. Intell. Lab. Syst. 37:525-530.
Henry, R.C., and C. Spiegelman (1997) Reported Emissions of Volatile Organic
Compounds are not Consistent with Observations, Proc. Nat. Acad. Sci.
94:6596-6599.
Henry, R.C., E.S. Park, and C.H. Spiegelman (1999) Comparing a New
Algorithm with the Classic Methods for Estimating the Number of Factors,
Chemom. Intell. Lab. Syst. 48:91-97.
Hopke. P.K., et al. (2006) PM source apportionment and health effects: 1.
Intercomparison of source apportionment results, Journal of Exposure Science
and Environmental Epi. 16:275-286.
Kim, B.-M., and R.C. Henry (1999) Extension of Self-Modeling Curve Resolution
to Mixtures of More Than Three Components. Part 2: Finding the Complete
Solution, Chemom. Intell. Lab. Syst. 49:67-77.
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EPA Unmix 6.0 Fundamentals & User Guide
Kim, B.-M., and R.C. Henry (2000) Application of the SAFER Model to Los
Angeles PM10 Data, Atmos. Environ. 34:1747-1759.
Kim B-M and R. C. Henry. Extension of self-modeling curve resolution to
mixtures of more than three components. Part 3. Atmospheric aerosol data
simulation studies (2000) Chemometrics and Intelligent Laboratory Systems 52:
145-154.
Lewis, C.W.; Henry, R.C.; Shreffler, J.H. (1998) An exploratory look at
hydrocarbon data from the Photochemical Assessment Monitoring Network, J.
Air & Waste Manage. Assoc..48: 71 - 76.
Lewis, C.W.; Morris, G.; Henry, R. (2003) Source Apportionment of Phoenix
PM2.5 Aerosol with the Unmix Receptor Model, J. Air & Waste Manage. Assoc..
53: 325-338.
Mukerjee, S.; Morris, G.A.; Smith, L.A.; Noble, C.A; Neas, L.M.; Ozkaynak, A.H.,
Gonzales, M. (2004) Receptor Model Comparisons and Wind Direction Analyses
of Volatile Organic Compounds and Submicrometer Particles in an Arid,
Binational, Urban Air Shed Environ. Sci. Technol. 38: 2317 - 2327.
Kim B-M and R. C. Henry. Application of the SAFER model to Los Angeles PM10
data (2000). Atmos. Environ. 34:747-1759.
Park E.S., Spiegelman C, and Henry R.C. Estimating the number of factors to
include in a high-dimensional multivariate bilinear model (2000) Communications
in Statistics, Simulation & Computation 29:723 - 746.
Poirot, R.L., P.R. Wishinski, P.K. Hopke, and A.V. Polissar (2001) Comparative
Application of Multiple Receptor Methods to Identify Aerosol Sources in Northern
Vermont, Environ. Sci. Technol., 35:4622-4636.
Willis, R.D. (2000) Workshop on Unmix and PMF as Applied to PM2.s, U.S.
Environmental Protection Agency Report No. EPA/600/A-00/048, Research
Triangle Park, NC, June 2000.
Willis, R.D. W.D. Ellenson, T.L. Conner (2001) Monitoring and Source
Apportionment of Particulate Matter Near a Large Phosphorous Production
Facility, J. Air& Waste Manage. Assoc. 51: 1142-1166.
Xin-Hua Song, Alexandr V. Polisssar, Phillip K. Hopke, Sources of fine particle
composition in northeastern US (2001) Atmos. Environ. 35:5277-5286.
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APPENDIX A: INSTRUCTIONS FOR RUNNING UNDER WINDOWS VISTA
Installation of EPA Unmix on a machine with Windows Vista operating system
(OS) does not differ other operating systems. The installation still requires
system administrator privilege. However, Windows Vista users have an additional
constraint due to the inner workings of their OS. While users on Windows XP
machines can run EPA Unmix as regular users, users on Windows Vista
machines are required to run the machines as system administrators to be able
to run EPA Unmix. EPA Unmix will not run on Windows Vista without this
change.
To implement this, right mouse click on the EPA Unmix shortcut (found on the
desktop) and select the "Properties" menu option from the pop menu. A window
resembling the image shown here appears. Select the "Compatability" tab. In the
bottom of the tab sheet, check the "Run the program as an administrator"
EPA Unmix 6.0 Properties
General j Shortcut | Options [ Fort | Layout
Colors ] Compatibility j Security { Details
If you have problems with this program and it worked correctly on
in earlier version of Windows, select the compatibility mode that
matches that earlier version,
Compatibility mode
1 I Run this program in compatibility mode for:
Settings
I j Run in 256 colons
| 1 Run in 640 x 480 screen resolution
Q Disable visual themes
D Disable desktop composition
[I] Disable display scaling on high DPI settings
Privilege Level
IZ1 Run this program as an administrator
Ijf? Show settings for al users
OK
Cancel
checkbox (as showns above) in the "Privilege Level" section and press the "OK"
pushbutton. This will ensure that the user can run EPA Unmix program on their
machine.
The user should contact their system administrator if they are unable to execute
the above mentioned steps to avail themselves the ability to run EPA Unmix.
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APPENDIX B: INSTALLING A NEW VERSION OF EPA Unmix
If anyone wishes the install a new version of EPA Unmix when they already have
a version on their machine, use the following steps.
1) Double-click on the installation package and keep pressing "Next" until the
installation is complete.
2) Find the unmix6R_mcr sub-folder in the Program Files\EPA Unmix 6.0 folder
and delete the folder. Since this folder is created on the user's machine, deleting
does not have deleterious effect. It only ensures that this folder is correctly
generated on the user's machine.
3) Double-click on the icon titled EPA Unmix 6.0 on the desktop.
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APPENDIX C: VARIABILITY CALCULATION ALGORITHM
Unmix processes input data to produce feasible solutions by placing equal
weights on all chosen observations. An important aspect of the Unmix approach
is that the solution finding method is constructive in nature. That is, the model
first defines a solution space and follows it through with finding a "point" in space
that is called a feasible solution. Thus, in constructive models, it is imperative that
the construction technique that produced a feasible solution be confirmed by
other means. One of the more popular methods is the bootstrapping method.
(The complimentary process to construction is finding solution through a process
of elimination where a solution is singled out as the most feasible solution from
among a multitude of possible solutions.)
In constructive solution approach with equal weights criterion, the magnitude of a
few observations can have disproportional effect on the solution. The solution
may be a "point" at the edge of the feasible solution space. The absence of some
observations can either produce a solution point far away from the original
solution point (qualitatively different solution) or, in the worst case, place the point
outside the feasible solution space (non-feasible solution). Therefore, it is
important to investigate the certainty (or uncertainty) of the solution of interest
before proceeding to interpreting. We will, henceforth, refer the data set used to
obtain the feasible solution as the base data set. Variability estimates associated
with a feasible solution are computed using the bootstrap method. Data sets,
termed as bootstrap variates, are created by sampling the base data set. Each
variate is analyzed using the same model to obtain a range of values from the
bootstrap runs and thus the Variability associated with the feasible solution
obtained from the base data set.
Bootstrapping Method
Let X = [Xi, X2, X3... XN} be an N-observation vector where X, is an M-vector of
concentration measurements of M species. The vector X is assumed to have
temporal association in the following manner: The observations are the result of
analysis done on the specimen samples collected from a filter placed at a site of
interest. The samples can range from 30-minute averages to daily averages. In
some rare cases, data from multiple sites may be present. In those cases, it is
hard to classify the time interval of the input data set.
Based on the data set, a subset of the species and observations are chosen for
further analysis to determine the source of the species. Source apportionment
models such as EPA Unmix may be used to analyze the data to suggest
composition and contribution matrices for the chosen set of species and
observations. Using the composition matrix, sources can be identified by known
signatures of well known sources. In Unmix, the presence of a composition and
its associated contribution matrices is called a feasible solution for the chosen set
of species and observations. This pair of composition and contribution matrices
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EPA Unmix 6.0 Fundamentals & User Guide
will be called the base feasible solution. This solution can be analyzed for its
robustness using the bootstrap runs.
An important detail in creating the bootstrap variate is the sampling method. If the
observations were samples from an independent, identically distributed random
distribution, simple sampling techniques should suffice. But, the data sets used in
source apportionment models are time series data that can be categorized as
dependent data. Simple sampling techniques can create bootstrap variates that
vary intrinsically from the base data set and lead to incorrect Variability
estimates. Serial correlation, defined as the statistical dependence of a datum on
its predecessors, is the most important intrinsic quality of time series data. Block
sampling of the base data produces bootstrap variates that preserve serial
correlation of time series data. The next important and obvious question is to ask
what optimal block length produces an acceptable bootstrap variate. The block
length that produces the bootstrap variates that is qualitatively and quantitatively
comparable to the base data set is called the optimal block length. The
quantitative requirement is easily defined. The size of the bootstrap variates must
be the same as the base data set. Qualitative comparisons between the data
sets are harder to define. We will address that later in this document. It is worth
noting that that optimal block length alone will not be enough to produce
qualitatively comparable data sets. However, it is a step in the right direction.
Block Length Calculation Schemes
Various schemes have been suggested to derive the optimal block length for a
given data set. Many of them involve using a statistical quantity of a bootstrap
variate with the same statistical quantity of the base data set. Frequently
mentioned statistics are bias or variance, one-sided probability, two-sided
probability, and auto-correlation.
Among the schemes to arrive at a reasonable block length to build bootstrap
variates, we will compare two schemes that help decide on the optimal block
length. One is based on the trial and error estimation using one of the three
parameters associated with a data set: variance, one-sided and two-sided
distribution as described in the paper titled "On blocking rules for the bootstrap
with dependent data" by Hall, Horowitz and Jing (1995). This method will be
referred as variance estimation method. The other method is based on the
spectral estimation via a flat-top lag-window as described in the paper titled
"Automatic Block-Length Selection for the Dependent Bootstrap" by Politis and
White (2004) and will be referred as the spectral estimation method.
Using a fixed block length for all data sets or even a step function approach to
fixing the block length can have deleterious effects. For instance, using a block
length of 3 can produce bootstrap variates that are much more similar to the
base data set. In the example data set, it was found that the maximum deviation
of the bootstrap variates generated using block length of 3 were consistently
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EPA Unmix 6.0 Fundamentals & User Guide
lower than the maximum deviation of bootstrap variates generated using block
length suggested by one of the two methods. In other words, bootstrap variates
using the block length of 3 produced variates more similar to the base data set
more often. While a block length of 3 may be appropriate for some data sets,
caution should be exercised when determining the block length of each base
data set.
Block Length Calculation - Variance Estimation Method
Hall, Horowitz and Jing (1995) have shown that the choice of the optimal block
length for dependent data depends significantly on the yardstick chosen to
measure the quality of a bootstrap variate. They have shown that the optimal
block length is of o(N1/3) when the yardstick used to compare is either the bias or
the variance, o(N1/4) when one-sided distribution is used and o(N1/5) when two-
sided distribution is used as the yardstick. The symbol o() implies a proportional
relationship. That is, when bias or variance is used as the yardstick, the optimal
(*) block length L* = k N1/3 for some positive constant k.
The following recursive algorithm is suggested to obtain the optimal block length
value:
The algorithm suggests using a "seed" block length first to obtain the estimates of
the chosen statistical quantity. Then, choose subsets of the base data set and try
all other block lengths smaller than the seed block length. Isolate the size of the
specific subset and its block length that has the minimum value for the chosen
statistical quantity, and then create the next iterate for the block length. Use this
iterate as the new seed and follow the procedure detailed above. When the seed
and the computed block length obtained from the seed are sufficiently close, the
iteration is stopped and the current value of the seed to considered the optimal
block length.
Block Length Calculation - Spectral Estimation Method
Politis and White (2004) have detailed a method based on spectral estimation to
suggest an optimal block length. A plug-in method is suggested to derive at an
optimal block length for a given data set. This method appears to factor the serial
correlation aspect of the given data set to derive the optimal block length. The
yardstick used to measure the quality of a bootstrap variate is the variance. As in
the Hall, Horowitz and Jing (1995) paper, Politis and White (2004) show that the
optimal block length is of o(N1/3). The plug-in method suggests a formula to
compute the constant of proportionality. The formula suggests optimal block
length in the L* is given by
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EPA Unmix 6.0 Fundamentals & User Guide
2G
N~3,
where
G=
the flat-top lag window is following function given by
Also,
1.5
0.5
-0.5
Flat top lag window ^
-2 -1.5
-0.5
0.5 1 1.5 2
and
n
M
In addition,M = 2m, where m is the smallest value of m such that
i(m + k) \< 2 |l2i^ for k = 1... 5 where
V N
p(k) =
R(G)
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EPA Unmix 6.0 Fundamentals & User Guide
Input Data for Block Length Calculation
There are two schools of thought on the type of input data that should be used in
calculating the optimal block length. One approach is to use the input
concentration data (Measured) and its serial correlation structure to obtain the
optimal block length. The other approach is to use the matrix obtained from
multiplying composition matrix by the contribution matrix. This matrix is referred
as the predicted concentration. The difference between the predicted and
measured concentration data are the so-called residuals.
In EPA Unmix, the use of measured concentration is preferred over predicted
concentrations for the following reasons. First, EPA Unmix differs conceptually
from other models that use input data uncertainty information. The spirit of EPA
Unmix is to use the data as provided by the user without any modification. Since,
predicted data can be viewed as reconstructed data, use of predicted data in the
bootstrapping algorithm violates this spirit. Secondly, the choice of measured
concentration versus predicted concentration is similar to the choice of evaluating
the algorithm's sensitivity versus the solution's sensitivity. The use of the
predicted concentrations can underestimate uncertainties since the input data
(predicted concentrations) to the bootstrap procedure tends to be less noisy
when compared to the measured concentration. Bootstrap variates constructed
from predicted concentrations can have qualitatively different underlying noise
structure compared to the bootstrap variate constructed from measured
concentrations.
Block Length Calculation Evaluation
In the experiments conducted using different sized data sets and criteria, the
spectral estimation appeared to be stable. The variance estimation method failed
with noisier data sets. The block lengths suggested by the variance estimate
method were sometimes larger than the number of observations in the data set.
Real data challenges algorithms since the noise found in real data is colored and
not white in nature and hence does not cancel out intrinsically. The spectral
estimation method fared better with noisy data sets compared to the variance
estimation method.
This conclusion was reached using known information about the particular data
sets such as the data collection interval, etc. In addition, using the block length
suggested by the spectral estimation method reduced the number of total
attempts to get 100 feasible solutions. That is, more quality variates were
generated using the block length suggested by the spectral estimation method.
The source apportionment model tends to reject variates by stating that no
feasible solution can be found when it fails to define the space in which a
possible solution can exist.
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EPA Unmix 6.0 Fundamentals & User Guide
Nevertheless, this experiment cannot guarantee success of one method over the
other for all types of data sets. In this, the evaluated algorithm shares the
following critical characteristic of any scientific approach: There is a possibility of
the existence of a real data set that can stump the model algorithm and the
model remains relevant only as long as the algorithm can be tweaked to meet the
new challenges.
Input Bootstrap Variates Analysis
The basic aim of the bootstrap method is to run the model a number of times
using altered versions of the base data set called the bootstrapped variates.
Bootstrapped variates are created by sampling the base data set with
replacements. By feeding the model with bootstrapped variates and by using the
resulting variations in the source compositions, the stability of the base data
sources can be confirmed. An issue of vital importance is the nature of
bootstrapped variates. Currently, all sets generated using the abovementioned
sampling scheme are considered valid. However, it is likely that the bootstrapped
variate might not exhibit the underlying features of the base data set. An extreme
case can result when a small percentage of the observations from the base data
set are used to generate the bootstrapped variate. Other cases might include the
more frequent occurrence of known outliers. Although, outliers are part and
parcel of any realistic data, excessive occurrence can substantially change the
nature of the data set resulting in sources unrelated to the base data sources and
therefore not a valid variation of the base data set. Using this and other data sets
differing qualitatively from the base data set (a.k.a. rogue data sets) is akin to
introducing a new data set in the middle of a bootstrap run.
The other extreme is when the bootstrap variates appears to be only a slight
variation of the base data set. This leads to a different problem of not adequately
testing the solution. These variates have to be ignored as well.
Thus, it is imperative that bootstrap variates be analyzed and confirmed to have
the similar but measurably distinct underlying features as found in the base data
set prior to feeding the bootstrap variate to the model for evaluation.
A possible argument against such analyzing of bootstrap variates is that this
process tends to underestimate uncertainties. This argument is vacuous on two
counts. First, one needs to know the unknown (Variability) to suggest that the
computed result is an underestimation (of the unknown). It is impossible to guess
even the range of the uncertainties due to the mathematics used in the model
and the sampling process to suggest possible sources. Secondly, this process
ensures that the uncertainties are more believable since only quality variates are
fed into the model, and the resulting solution is evaluated impartially. Thus,
analyzing the input bootstrap variate can only help produce a more justifiable
picture of the Variability associated with a chosen solution.
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EPA Unmix 6.0 Fundamentals & User Guide
In the experiments that have been conducted, the Variability range (2.5th
percentile and 97.5th percentile) obtained from the analyzing input variates have
both decreased and increased when compared to the results obtained without
any analyzing process. Thus, the argument that the analyzing process tends to
underestimate Variability is again found to be without merit.
An alternative to this process is the post-screening of the resulting solutions. The
bootstrap variates are used as generated by random sampling of the base data
observations with replacements, but the resulting bootstrap source compositions
are screened for its proximity to base source compositions. Such selective use of
bootstrap run results may violate the principles of the bootstrap approach of
analyzing base solutions and therefore lead to a less believable Variability
picture.
Analysis Method of Bootstrap Variates
Using a random number generator, a number ranging between 1 and the total
number of observations in the base data set is generated. The block of
observations of the size suggested by spectral estimation (as the optimal block
length) starting from that number is chosen for the bootstrap variate. Continue
this process of generating a random number and stringing together the block of
observation from the base data set until the size of the bootstrap variate equals
the size of the base data set. The block length guidance is ignored if there are
not enough observations available from the current starting point. That is, if N is
the number of observations and K is the block length, then any random number
R greater than N-K will have only N-R+1 observations available.
Use this bootstrap variate to be compared to the base data set using the
Generalized Singular Value Decomposition (GSVD) method. Let B be the base
data set and Bn be the nth bootstrap variate. Then, by using the GSVD method,
B and Bn can written as
B = U*C*X'
Bn = V*S*X'.
In the above expression, U and V are unitary matrices, X, a (usually) square
matrix, and nonnegative diagonal matrices C and S such that
C'*C + S'*S = I,
where I is the identity matrix. The matrices C and S can be viewed as the cosine
and sine decomposition matrices. Hence, the angular distance between the data
sets is
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EPA Unmix 6.0 Fundamentals & User Guide
structure of the base data set. Thus,
is the appropriate angle interval so
where cm and sm are the mth entries in the C and S diagonal matrices
and#m indicates the relative closeness of the mth common "factor" between the
two data sets.
The closer the angles are to zero indicates positive alignment or similar nature of
the underlying structure of the base data set and bootstrap variate while angles
that tend toward — shows almost no alignment of the underlying structure of the
4
data sets. In this model, bootstrap variates whose maximum angular deviation
from base data set structure does not exceed — are considered too similar to
50
the base data set and are rejected. Also, those bootstrap variates whose
minimum angular deviation from the base data set exceeds — are considered
8
too dissimilar and are also rejected. This requirement allows a generous amount
of variation on the base data set with 5% to 50% variation on the underlying
n n
40 8
that noise is a factor and ensures that the bootstrap variates are more than being
just minor variations of the base data set while retaining the underlying structural
features of the base data set.
Base Data Set Classifications
The underlying nature of the base data set dictates the nature of the bootstrap
variates in terms of their proximity to the base data set. For instance, if a base
data set has localized high values, good bootstrap variates, as described in the
earlier section, may be harder to produce. In such cases, the base data is
adjudged to be relatively rigid in its structure. Therefore, the base data set can be
classified into three categories based on their structural rigidity of "High",
"Medium" and "Low". If the base data set values are not localized, then a good
bootstrap variate may be produced with high probability. Such data sets are then
termed to have "Low" rigidity associated with its structure. We quantify the
classification using the following method.
All angular data associated with a bootstrap variate of all rejected bootstrap
n n
variates are collected. If the median value falls with the interval
then the
base data set is classified as "Low". If the median falls within the interval
n n
~6 ~5
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EPA Unmix 6.0 Fundamentals & User Guide
then the base data is classified as "Medium". Otherwise, the base data is
classified as "High."
All data sets have high and low values. The angle intervals are used to quantify
the possible significance of a small set of observations while generating
bootstrap variates. If a small set of values have disproportionate effect on the
generation of bootstrap variates, then the base data set is deemed to be either in
the "Medium" or "High" category in terms of its rigidity in its underlying structure.
Suspension of Bootstrap Variates Analysis
Also, in the interest of speeding up the bootstrap process, the model suspends
analyzing the bootstrap variates under the following circumstance: If the number
of rejected bootstrap variates does not exceed five(5) after the first twenty
five(25) attempts, then any further analysis of bootstrap variates are suspended.
The assumption behind this decision is that the initial low probability of obtaining
a poor bootstrap variate implies the base data and bootstrap creation procedure
are both robust and will produce high quality end results even without the
analysis of the bootstrap variates.
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EPA Unmix 6.0 Fundamentals & User Guide
APPENDIX D: PROCEDURE DIAGRAMS
85
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Appendix C - Unmix Procedure Diagrams
Data Processing
CO
-I—'
CD
Q
Select File
File Format
(see Table 1)
CD X
O UJ
2
CD
Q
Descriptive
Data
Statistics
Suggest
Exclusion
«£l
CD "- £
" CD CD
O
View Time
Series Plots
View/Edit
Observations
- Delete
Observation
Jr_
View/Edit
Observations
- Delete Point
View/Edit
Influential Points -
elete Poin
Identify
Influential
Points
-\
Delete
Influential
Points?
CD 5 CD
" ^ -S
28S
IJ- CD
Replace Deleted Points
CD
Q
Analyze Run -
Input Data Used in
this run
Data
Processing
Report
Run
-------
Appendix C - Unmix Procedure Diagrams
Initial Species Selection (Species with high average concentrations)
Evaluate Data
Recommended
Number of
Sources
Input # of Sources
No Partia So ution
Partia So ution
Feasible
Result
Select Feasible
Result from list
No Feasible
Solution
Q No Total
Total
V. Speceis
Evaluate Run
-------
Appendix C - Unmix Procedure Diagrams
Evaluate Run
_CD
^
2
CL
1
o
Analyze Run - Results
Source Compositions
Diagnostic Plots - Results
Source Composition
sources look reasonable based on the
Dotential sources impacting the site?
a. .2
o -g
o
O
Analyze Run - Results
Source Contributions
Analyze Run - Evaluation Source
Contribution Correlations
Diagnostic Plots - Results
Source Contribution
Evaluate sources with only a few
spikes in more detail
E 1
O CO
o
w
Analyze Run - Evaluation
Source Composition
Variability and
Distribution
Diagnostic Plots - Results
Source Composition Variability &
Variability Distribution
Evaluate sigma, distribution, and ranked value output to
letermine if species are significantly contributing to sources
and that the variability is reasonable.
CD
'O
CD
Q.
Analyze Run - Evaluation
Fit Diagnostics
Diagnostic Plots - Results
Fit Diagnostics,
Standardized Residuals
Remove Species with r2 values < 0.30, #
of runs for 100 feasible solutions should be
less than 150 (med. size), and evaluate species with
species with standardized residuals > 3
_o
Q.
CD
O)
•a
LU
Analyze Run - Evaluation
Source Composition
Variability Distribution
Diagnostic Plots - Results
Source Composition Variability
Distribution,
Edge Plot
Evaluate sources with high
variability and determine if the sources have a
low number of edge points
Export Results
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