User's Guide for MCestimate
Matthew Etterson
U.S. Environmental Protection Agency
12 September 2013
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Contents
1. Preliminaries 3
1.1 Disclaimer & distribution 3
1.2 What is MCestimate and why is it needed? 3
1.3 Installation 4
2. Data format 5
2.1 Required data 5
2.2 Formatting requirements 5
2.3 Example: SimData.xls 6
3. Getting your data into MCestimate 7
3.1. The File Menu 8
3.2 Importing nest data 9
3.3 Viewing import errors 13
3.4 Re-describing the data after fixing errors 14
3.5 Opening a saved nest file 14
3.6. Displaying summary information 15
3.7 Exporting a file for analysis in program MARK 15
4. Modeling nest failure 16
4.1 Specifying the response distribution 16
4.2 Overview: designing models 17
4.3 Building models by specifying covariates 17
4.4 Importing models from a file 21
4.5 Running the models 22
4.6 The Pending models context menu 22
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5. Interpreting model results 24
5.1 Model convergence 26
5.2 Parameter estimates 26
5.3 Goodness-of-fit 30
5.4 Example. Assessing Goodness-of-fit 32
5.5 Exporting MCestimate results 35
5.6 Visualizing MCestimate results 37
6. Managing results tables and model lists 38
6.1 Saving an AIC Table 39
6.2. Saving a model list 39
6.3 Managing lists 39
Acknowledgments 40
Literature cited 40
1. Preliminaries
1.1 Disclaimer & distribution
Thank you for your willingness to try MCestimate. This is a work in progress, so expect some bugs! If
you report them I will do my best to fix them quickly. However, your use of this program is at your own
risk.
Matt Etterson
etterson.matthew@epa.gov
218-529-5158
1.2 What is MCestimate and why is it needed?
MCestimate is a tool for estimating probabilities of failure in the presence of competing risks. It was
originally developed to facilitate the study of causes of avian nest-failure. However, competing risks
arise in virtually all stochastic processes and MCestimate can be applied in many contexts outside of
avian nest failure. For example, carcass distribution trials are a commonly used technique for
understanding either scavenging rates or searcher efficiency to better understand animal mortality as a
result of collisions with anthropogenic structures such wind turbines, automobiles, power lines, or
3
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windows. The two fates (scavenged versus discovered) can be viewed as competing risks. Similarly,
standard toxicity tests generally include a control treatment in which some animals die due to natural
causes or experimental stress that is not related to the toxicity of the test material. These two sources
of mortality (intoxication versus control) are competing risks. MCestimate can be (indeed is being) used
to understand both of these processes. However, for historical reasons and for simplicity of
presentation, this user's guide, and many of the menus in MCestimate explicitly refer to the analysis of
nest survival data.
MCestimate uses nest-monitoring data to estimate daily and overall probabilities of nest-failure due to
specific causes (competing risks). It is programmed in MATLAB (Mathworks 2012a) and compiled as a
standalone program. However, other good computer programs (White and Burnham 1999, Dinsmore et
al. 2002) and code for statistical software (Stanley 2000, 2004a; Shaffer 2004) already exist for
estimating daily survival rates for nests when nest outcomes are classified binomially (success/fail).
Fewer methods exist for nests with multinomial outcomes (success, depredated, adverse weather,
abandonment, etc.). Multinomial methods are slightly trickier than their binomial counterparts because
estimating the probabilities of failure due to a given cause, requires that you correctly consider the
probabilities of not failing due to all other possible causes. When combined with the need to account for
nests not being monitored daily, this gets trickier still. MCestimate does this using the Markov chain
algorithms described by Etterson et al. (2007a, 2007b). Like other current nest survival methods,
MCestimate is a generalization of Mayfield (1961, 1975) methods for estimating daily probabilities of
failure. The primary generalizations of MCestimate over the Mayfield (1961, 1975) methods are:
1. MCestimate does not require exact knowledge of the timing of failure events (i.e., daily
nest-monitoring is not required).
2. MCestimate allows separate estimation of daily probabilities of failure due to multiple
causes (competing risks, or cause-specific failure).
3. MCestimate allows separate specification of covariates to different fates to explore
hypotheses about the influence of environmental conditions on cause-specific failure rates.
MCestimate is also a simple multistate model (see Hougaard 1999 and Pradel 2005 for details on
multistate and multievent models). Other software for fitting multistate models is also available
(Choquet et al. 2004, 2009), which can accommodate more general models than MCestimate.
MCestimate has been designed for easy use with an intuitive graphical user interface.
1.3 Installation
MCestimate installation requires 2 files. The MATLAB Compiler Runtime (MCRInstaller.exe) installs a
library of MATLAB functions that are used by components built in the MATLAB environment. The MCR is
specific to the version of MATLAB in which MCestimate was compiled. This build of MCestimate used
version 7.14.0.739, which is associated with MATLAB 2012a (32-bit). This file can be downloaded from
the Mathworks website (http://www.mathworks.com/products/compiler/mcr/). Installing the MCR is a
one-time event and should not need to be repeated until MCestimate is compiled under a new version
of Matlab. Note that to install the MCR you will need administrative rights to your computer. To install,
double click on the file MCRInstaller.exe. This will call a setup program that you should click through.
Once the MCR is installed you should be able to run MCestimate by double-clicking the file
MCestimate.exe. The initial distribution ([insert URL for MED website, (pending)]) consists of the
following four files:
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1. MCestimate.exe
2. MCestimateUsersGuide.pdf
3. SimData.xls
4. SimDataBad.xIsx
2. Data format
MCestimate is designed to import nest monitoring data from Microsoft® Excel. For importing, your nest
data should be arranged with one nest per spreadsheet row. The order in which columns occur is
somewhat flexible, but with the following rules: 1) the first (left-most) column is reserved for an
alphanumeric nest identifier, and 2) the monitoring data (the actual nest visit dates) must be in the
right-most columns.
2.1 Required data
1. Row of unique headers for all columns.
2. Column giving the ultimate fate of each nest (successful, depredated, weather, etc.). You may
have as many fates as you wish. However, "unknown" is a treacherous one. Be careful with it!
3. Columns (at least two) giving the dates on which each nest was visited.
a. The first column gives the first date on which the nest was observed to be active.
b. The last column gives the date of the last visit to the nest.
Because there are many ways to code and interpret nest-monitoring data, I recommend the
following rules. Note that I define an "observation" on a nest to be a set of two successive
nest visits.
i. For all nests, the first observation should begin with the first visit on which a
nest was known to have contents that could fail (eggs or nestlings). The first
observation should not begin with nest construction.
ii. For all nests, if a nest was sufficiently developed to have fledged during an
observation, then the second visit of the observation should be discarded and
the fate of the nest should be recorded as its state on the first visit of the
observation (presumably "successful"). To see why this is important, read
Stanley (2004b).
Optional data include:
4. Columns giving covariate data (year, treatments, etc.)
5. Column giving the age of a nest on the first visit (where "first visit" is defined as 3.b.i., above).
2.2 Formatting requirements
Two example data sets (SimData.xls & SimDataBad.xIsx) are provided in the dropbox foloder (Fig. 1).
The data in SimData.xls were simulated using fewer covariates than are actually provided in the data.
SimDataBad.xIsx was created from SimData.xls by changing two data values to produce two common
5
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types of errors. Each of the examples in this user's guide uses one of these two files, so you should be
able to reproduce the examples exactly. You might also have some fun trying to figure out which
covariates I actually used to generate the data (and what the "true" parameter values were).
1. Dates should be given in the following format "Ol-Apr-09." Deviations may work (e.g.
"01/04/09"), but employ them at your own risk!
2. There must be no missing data from any columns used for analysis (except visit dates). For now
this is a very strict limitation. Cells with missing data will be assigned to the status "NaN" (not a
number). If you import a spreadsheet with missing data, the program will display an error
message and you will be unable to perform any analyses until the missing data is supplied or the
nests with missing data are removed.
3. For each nest, visits are numbered sequentially beginning with the first active visit to a nest and
ending with the last visit. Thus there won't be the same number of visits to each nest. All cells
to the right of the last visit to a nest should be left blank.
4. The nest data must be on the first worksheet in your Excel Workbook. Safest thing is to delete
all other worksheets.
5. Data may be saved in Excel 1997-2003 Format (*.xls) or Excel 2007 Format (*.xlsx, default).
6. Headers cannot include an asterisk. In general I'd recommend avoiding characters other than
numbers and letters. I'd also recommend avoiding having one header that is a proper subset of
another (e.g., don't have "Fl" and "F12"). It would probably be fine, but it might not...
2.3 Example: SimData.xls
Figure 1. Example data SimData.xls
njj J""" '
—' Horn* Irv.-rt Pagt Urout Formula! Data RnWw unv Aoo.lm »
1
2
3
10
11
M =i a J ,^_ ::
uJ^t "ft™* Cv££T s££n
A B C D E F G
nest late yr hi in age VI
1 depredated 1 14.9 to 6 8-May-01
2 weather 0 11 0 to 9 15-Jun-OO
3 weather 0 9 1 to 1 15-Jun-OO
4 survive 0 9 7 hi 15 1-Jul-OO
5 survive 1 11 1 hi 11 12-Jun-OI
6 depredated 0 64 to 2 12-Jun-OO
7 depredated 0 10.7 hi 2 3-Jun-OO
8 depredated 0 13 4 hi 11 14-Jun-OO
9 survive 0 4 7 to 2 3-Jun-OO
10 depredated 1 14 5 to 12 28-Jun-01
12 11 survive 0 11 hi 14 12-JuKJO
13 12 weather 0 11 2 to 12 9-Jun-OO
14 13 survive 0 13 8 hi 11 2-Jul-OO
15
16
tee
187
IB
189
19
491
492
i-i -
494
495
191
497
196
499
ro-
501
502
503
14 depredated 0 63 to 5 4-Jun-OO
15 depredated 1 4 4 to 14 7-Jun-01
485 depredated 1 12.7 to 12 21-May-01
486 depredated 0 3 7 hi 6 19-Jun-OO
487 weather 1 13 1 hi 14 9-Jun-01
488 depredated 1 69 to 1 6-May-01
489 survive 1 5 8 to 8 24-Jun-01
490 depredated 1 80 to 12 19-Jun-01
491 depredated 0 94 to 4 22-May-OO
492 depredated 1 11 1 hi 6 24-May-01
493 survive 0 7 3 to 8 5-Jul-OO
494 survive 0 39 hi 15 15-Jul-OO
495 survive 0 13 5 hi 13 18-Jun-OO
496 survive 0 3 6 hi 3 22-Jun-OO
497 depredated 1 10-5 hi 5 ir>May-Ol
498 survive 0 10 9 to 4 30-Jun-OO
499 depredated 1 1 1 7 hi 7 7-Jul-01
500 survive 1 6 6 to 2 20-Jun-01
unuUBv
HJUig!
_ .
H
V2
12-May-01
19-Jun-OO
19-Jun-OO
4-JUI-OO
14-Jun-01
16-Jun-OO
7-Jun-OO
1 7-Jun-OO
7-Jun-OO
2-Jul-DI
15-Jul-OO
1 3-Jun-OO
6-Jul-OO
8-Jun-OO
9-Jun-01
23-May-01
21 -Jun-00
1 3-Jun-01
9-May-01
27-Jun-01
21-Jun-01
25-May-OO
26-May-01
7 Jul-00
18-Jul-OO
22-Jun-OO
24-Jun-OO
12-May-01
3-Jul-OO
10-Jul-01
24-Jun-01
i ;: .
V3
21-Jun-OO
21 -Jun-00
8-Jul-OO
17-Jun-01
18-Jun-OO
9-Jun-OO
21 Jun-00
11-Jun-OO
6-Jul-01
1 9-Jul-OO
15-Jun-OO
9-Jul-OO
11-Jun-OO
12 JuiiO!
25-Jun-OO
16-Jun-01
1-Jul-Q1
24-Jun-01
27-May-OO
20 l.'ay 01
9-Jul-OO
21-JuUX)
26-Jun-OO
27-Jun-OO
14-May-oi
7-Jul-OO
215 .inn 01
V4
25-Jun-OO
21-Jun-01
22-Jun-OO
23-Jun-OO
1 3-Jun-OO
1 7-Jun-OO
12-JUr-OO
27-Jun-OO
5-JuM31
27-Jun-01
29-May-OO
1-Jun-01
12-Jut-OO
24-Jul-OO
29-Jun-OO
1 -JuMJO
16- May -01
10-Jul-OO
1-Jul-01
•
K L M N 0 P
V5 V6 W V8 V9 V10
28-Jun-OO 2-Jul-OO 4-Jul-OO 7-Jul-OO
24-Jun-01
27-Jun-OO
16-Jun-OO 18-Jun-OO 20-Jun-OO 23-Jun-OO
20-Jun-OO
H
1-JuHX) 5-Jul-OQ
9-Jul-01
29-Jun-01
2-Jun-OO
5-Jun-01
15-Jul-OO 18-Jul-OO 20-Juf-OO
3-Jul-OO 7-Jul-OO 11-Jul-OO 13-JuMX)
19-May-O! 22-May-O! 25-May-Ol 29-May-Ol
1 3-Jul-OO 1 7-Jul-OO 20-Jul-OO
3-Jul-01 6-Jul-01 10-Jul-01
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Fig. 1, above, shows portions of the sample data file SimData.xls. The sample file has 16 columns of
data as described in Table 1.
Table 1. Simulated nest-monitoring data in SimData.xls
Column header Description
nest Unique identification number for a nest. Can be any combinations of letters, spaces,
and numbers.
fate Ultimate fate of the nest (assumed to be determined on last visit).
yr Year of study in which nest occurred, to be used as a covariate.
ht Nest height (m) above ground.
trt A treatment thought to influence predation rate (hi vs. lo).
age Age (d) of the nest on the first visit (VI).
V1-V10 Columns of dates of nest-visits to nest. VI is the first visit on which nest could have
failed (i.e. the first visit on which the nest had eggs or nestlings observed).
3. Gettingyour data into MCestimate
Start MCestimate by double-clicking MCestimate.exe. You should now be looking at the main
MCestimate window (Fig. 2).
Figure 2. The main MCestimate window at startup
File Analysis About
Expiration date: -
Status
Ready
Fitted models:
Decimal precision: 2
Response Variable:
Interrupt
O Binomial (success/fail) O Multinomial
Pending models:
Model name
ML AICc | delta AICc | Weight
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Operations concerned with importing, managing, and formatting data for MCestimate are initiated via
the File menu in the upper left corner (Table 2). The Analysis menu is described in Section 4: Modeling
nest failure. After analysis, most operations are initiated via the Fitted models context menu (Section
5). The About menu provides information on the build date of the current version. Ultimately it will also
provide a recommended citation.
Table 2. MCestimate menus
Menu Item
Description
File
Analysis
About
Set of commands for importing and formatting data for MCestimate.
Set of commands for performing analysis and managing output.
Information about MCestimate.
3.1. The File Menu
The File menu in MCestimate has 8 choices most of which are designed to assist with importing,
formatting , viewing, and exporting data (Table 3, Fig. 3).
Table 3. The File menu
Menu Item
Description
Set working directory
Import data
View file
Open data file
Display summary info
Export MARK file
Clear data
Exit
Sets the default directory for files for a given project.
Opens a file browser to select a data file for importing. If a file is chosen,
subsequently launches the DescribeData GUI (Fig. 4, below).
Displays the MCestimate version of the Excel file. This is used for fixing data
errors.
Opens a properly formatted MCestimate file created via the Import data
option.
Displays summary information about the current data file.
Exports an encounter history file (*.inp) for analysis in program MARK.
Clears all nest data from memory. Do this before opening another nest file.
Exits MCestimate.
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Figure 3. The Main MCestimate window showing the File menu
Analysis About
Set working directory
Import data
View Pile
Open data file
Display summary info
Export MARK file
Clear data
-Status-
Ready
j
Decimal precision: 2
Interrupt
Model name
Model name
delta AICc
Weight
3.2 Importing nest data
To import a spreadsheet into MCestimate, choose the Import data option from the File menu. This will
call up a typical windows file browser (Fig. 4) that will display only Excel 2007 (*.xlsx) files. Excel 1997-
2003 (*.xls) files can be viewed by changing the type at the bottom of the file browser (Files of type:).
Figure 4. Select your data file browser
Select your data file. f?l(E]
Look in:
a
My Recent
Documents
\J
Desktop
»
My Documents
;l
My Compute*
^
My Network
Places
LJ MCestimale _~] •- S) d* B-
S}simData.xls
"S]5imDataBad.xlsx
File name: _^j Open
Files of type: | (".*"! ^\ Cancel
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After you choose your file and click open, MCestimate will automatically open the DescribeData
window (Fig. 5). If you load SimData.xls, your DescribeData window should look like Fig. 5.
Figure 5. The DescribeData window
Variables:
nest
fate
y
ht
lit
age
V1
V2
V3
V4
V5
V6
V7
V8
V9
V10
*
- Observed States:
State variable » |
Monitoring data:
1 1
All Fates:
A
v
Success »
Column indicating first observation »
Age of subject on first observation
- Save to MCestimate file:
Source file:
— Independent variables (covariates)-
Categorical predictors:
Save MCestimate file
Clicking the above button will open a
standard dialog box for saving files.
Reset
Close
When the DescribeData window loads, the data columns of your spreadsheet should be listed in the
Variables listbox and all other boxes should be empty. Before you can analyze your data, you must
identify its structure to MCestimate. Not all of the controls on this page must be used.
The required controls are:
1. You must identify the column containing nest outcomes (State variable). In SimData.xls (Figs. 1,
5) it is the variable labeled fate (but you may use any label you wish). Enter it by selecting the
variable in the Variables box and clicking the Fate variable » button. Once you do so, the All
Fates listbox will contain a list of all entries in that column of the spreadsheet. If you make a
mistake, don't worry. In most cases you can simply highlight the correct variable and click the
button again and the incorrect entry will be replaced. If you manage to screw up completely,
then you can click the Reset button and start over!
2. You must indicate which one of the fates corresponds to a successful nest. Do this by
highlighting that fate in the All Fates listbox and clicking the Success » button.
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3. You must identify the monitoring data by indicating which column contains the first nest visit.
This is done by highlighting the proper variable (in SimData.xls it is VI, though again you may
use any headers you wish) and clicking the button Column indicating first observation.
4. You must name the data and save it as a MCestimate file. Do this by clicking the Save
MCestimate file button. This will close the DescribeData window and you should see a
message in the main MCestimate window Status box "Parsing data ..." If you have a lot of data
this could take a minute or two. After parsing, the DescribeData window will close and a file
browser will open to allow you name and save the file. Once the file is saved, a status message
will be displayed (Fig. 6). If the parsing algorithm fails, the file browser will not open and a
status message will let you know about data formatting problems. Dealing with failed imports is
the topic of Sections 3.3 and 3.4 below.
Figure 6. Status message after a successful import
CHI
The optional controls are:
5. Age of subject at first visit: If this is known it can be entered using the button of the same
name.
6. Categorical predictors: This listbox is used to identify categorical covariates.
7. Quantitative predictors: This listbox is used to identify quantitative covariates. Note: Integer-
coded covariates may be entered as either categorical, quantitative, or both. If you code an
integer-valued variable in both ways for the same analysis MCestimate will either append (c) for
categorical, or (q) for quantitative to the name of the variable. For most integer-coded variables,
the choice will be obvious about whether to specify that variable as categorical versus
quantitative. However, for ordinal variables, in which the codes 1, 2, 3,..., n indicate a
meaningful progression (e.g., over time, as in years, or from small to big, as in size classes), you
might wish to explore both kinds of effect. The best example I can think of to justify exploring
both kinds of effects in a single variable is with a "year" effect. Years may randomly fluctuate in
predation pressure or weather events, arguing for a categorical coding. On the other hand,
years may follow a trend, arguing for a continuous effect. In the end the choice should best
reflect why you want to use the variable as a covariate.
Example: importing SimData.xls
From the File menu choose Import Data and open SimData.xls. Then, using the DescribeData window,
add variables following the rules above until the DescribeData window looks like Fig. 7. Then click Save
MCestimate file.
11
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Figure 7. The DescribeData window for the importing data example
Variables:
inest
tfl
ht
age
V4
r
JV6
V7
JVB
V9
V10
Observed States:
- Monitoring data: -
State variable »
Column indicating tirst observation »
Age of subject on first observation » |
- Independent variables (covariates) -
Save to MCestimate file: -
Source (lie:
Save MCestimate tile
Clicking the above button will open a
standard dialog box for saving files.
Example: importing SimDataBad.xlsx
This example is designed to illustrate the primary causes for failures in data importing. They are 1) nest
observations lasting zero or negative days, and 2) missing data. The parsing algorithm searches for both
kinds of errors. If either occurs then the status dialog reports the identification numbers of all nests
having one or the other error. For an example, follow the steps above to import data, but this time
choose SimDataBad.xlsx. After parsing, the status dialog should look like Fig. 8 (below).
Figure 8. Status message after a failed import
ImportErrors
Your data contain errors that will crash MCnestimate.
Nests with missing data: Nests wJh observations < 1 day:
1
1
1
11
1
12
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3.3 Viewing import errors
If you have many errors, you will probably want to edit your Excel file and re-import the data. However,
if there are only a few errors, or you don't wish to alter your Excel file, you may do some limited editing
in MCestimate. This is done by choosing View file under the File menu. Doing so for this example will
produce a new window that should resemble Fig. 9.
Figure 9. The imported nest file for SimDataBad.xIsx
Edi
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
123456789
nest fate yr ht trt age VI V2 V3
1 depredated 1 14.861410 65/8/2001 5/12/2001 NaN
2 weather 0 10.967410 96/15/2000 6/14/2000 6/21/2000
3 weather 0 9.0823 lo 16/15/2000 6/19(2000 6/21/2000
4 survive 0 9. 6552 hi 157/1/2000 7/4/2000 7/8/2000
5 survive 1 11. 11 72 hi 116/12/2001 6/14/2001 6/17/2001
6 depredated 0 6.4027IO 26/12/2000 6/16/2000 6/18/2000
/depredated 0 10.6757 hi 26/3/2000 6/7/2000 6/9/2000
8 depredated 0 13.4008 hi 116/14/2000 6/17/2000 6/21/2000
9 survive 0 4.6667IO 26/3/2000 6/7/2000 6/11/2000
10 depredated 1 14.516510 126/28/2001 7/2/2001 7/6G001
11 survive 0 NaNh] 1 4 7/1 2/2000 7/15/2000 7f1 9/2000
12 weather 0 11210110 126/9/2000 6ft 3/2000 6/15/2000
3 survive 0 13 8447 hi 11 71212000 7 IS/2000 7/9/2000
4 depredated 0 6.275210 56/4/2000 6/8/2000 6/11/2000
5 depredated 1 4.361110 146/7/2001 6/9/2001 6/1 2/2001
6 weather 1 5 6608 hi 37/2/2001 7/5/2001 7/8/2001
7 depredated 0 14 0732 lo 46/18/2000 6/22(2000 NaN
8 survive 0 14. 5480 lo 116/24/2000 6/27/2000 6/30/2000
19 weather 1 9.616710 116/28/2001 7/1/2001 7/3/2001
20 survive 1 13.847210 55/12/2001 5f!5/2001 5/17/2001
21 survive 0 58240IO 37(2/2000 7/6/2000 7/9/2000
22 survive 1 13.3541 hi 86/5/2001 6/12/2001 6/15/2001
23 survive 0 8. 41 95 hi 87/4/2000 7/8/2000 7/12/2000
24 survive 1 13.513810 105/14/2001 5/18/2001 5/21/2001
25 depredated 1 14. 8732 hi 136/8/2001 6/10/2001 6/12/2001
26 depredated 0 13. 6630 hi 55/16/2000 5/19/2000 NaN
27 survive 1 9.201 2 hi 147/3/2001 7/5/2001 7/7/2001
<
10
V4
NaN
6/24/2000
6/25/2000
NaN
6/21/2001
6/22/2000
NaN
6G3/2000
6/1 3/2000
NaN
NaN
6/17/2000
7/12/2000
6/15/2000
NaN
7/1 1 /2001
NaN
7/2/2000
7/6/2001
5/21 /2001
7/13/2000
6/18/2001
7/15/2000
5/23/2001
6/16/2001
NaN
7/10/2001
11 12 13
V5 V6 V7
NaN NaN
NaN NaN
6/28/2000 7/2/2000 7/4/2000
NaN NaN
6/24/2001 NaN
NaN NaN
NaN NaN
6/27/2000 NaN
6/16/2000 6/18/2000 6/20/2000
NaN NaN
NaN NaN
6/20/2000 NaN
NaN NaN
NaN NaN
NaN NaN
NaN NaN
NaN NaN
7.6/2000 NaN
7/10/2001 NaN
S/23/2001 5/27/2001 5/31 /2001
7/17/2000 7/21/2000
6/22/2001 NaN
7/1 7/2000 7/20/2000
5/27/2001 NaN
NaN NaN
NaN NaN
7/1 2/2001 NaN t v
>
•*
The status message (Fig. 8) reported an observation lasting zero or fewer days for nest 2. Looking across
the visit dates for nest 2, you can see that the date in row 3, column 8 is a day earlier than that in row 3,
column 7, which will generate an observation lasting -1 days. Similarly, the status message reported
missing data for nest 11. MCestimate represents missing data as NaN (not a number). Looking across
row 12, NaN appears in column 4 (ht). The correct values for these cells are 6/19/2000 and 7.2,
respectively (Fig. 1). These values can be typed directly into the cells. Alternatively you can use the Edit
menu (Fig. 10). If you simply want to remove all nests with errors, you can use the first two choices. If
you want to look at each error individually you can use the third or fourth choices Delete current cell
and Delete current row(s). In particular, try selecting the cell in row 3, column 8 and choose Delete
current cell. This will remove the value in the selected cell and shift leftward by one cell all cells to the
right of the selected cell. Because the incorrect date is nested within a sequence of successful (survived)
observations, deleting that particular cell will not affect the estimation results (but this will change in
future versions of MCestimatel). Choosing Delete row will remove the entire row (nest) from the data.
Deleting a row will always change the estimation results.
13
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Figure 10. The Edit menu in the NestFile window
Remove all nests with missing covariates
Remove all nests with an observation < 1 day
Delete current cell
Delete current rowi(s)
3674 lo
.0823 lo
6 5)8/2001
96/15/2000
1 6/15/2000
5)12/2001
6)14)2000
6)19)2000
6/21/2000
6/21/2000
6/24/2000
6125/2000
NaN
NaN
NaN
NaN
0
depredated 0
depredated 0 1
depredated 0 1
survive 0
depredated 1 1
survive 0
weather 0 1
survive 0 1
depredated 0
depredate.:! 1
weather 1
depredated 0 1
i survive 0 1
9 weather 1
20 survive 1 1
21 survive 0
22 survive 1 1
23 survive 0
24 survive 1 1
25 depredated 1 1
26 depredated 0 1
.6552 hi
.4027 lo
.6757 hi
.4008 hi
.666710
.516510
NaN hi
.2101 lo
.8447 hi
.2752 lo
.361 1 lo
.6608 hi
.0732 lo
.5480 lo
.616710
.8472 lo
.8240 lo
.3541 hi
.41 95 hi
.51 38 lo
.8732 hi
.6630 hi
27 survive 1 9.201 2 hi
157/1/2000
26/12/2000
2 6/3/2000
11 6/14/2000
2 6/3/2000
126)26/2001
147/12/2000
126)9/2000
11 7/2/2000
5 6/4/2000
146/7/2001
3 7/2/2001
4 6/1 8/2000
11 6/24/2000
11 6/28/2001
55/12/2001
3 7/2/2000
8 6)8/2001
8 7/4/2000
105/14/2001
136/8/2001
55/16/2000
14 7)3/2001
7/4/2000
6/16/2000
8)7)2000
8)17/2000
6/7)2000
7/2/2001
7/15)2000
6/13/2000
7)5/2000
6)8/2000
6)9/2001
7)5/2001
6/22/2000
6/27/2000
7)1/2001
5)15/2001
7)6/2000
6/1 2)2001
7)8)2000
5/18/2001
6/10/2001
5/19)2000
7)5/2001
7/8/2000
6/18/2000
6/9GOOO
6/21/2000
6/11/2000
7/6/2001
7/19/2000
6/15/2000
7/9/2000
6/1 1 /2000
en 2/2001
7/8/2001
6/30/2000
7/3/2001
5/17/2001
7/9/2000
6/15/2001
7/12/2000
5/21/2001
6/12/2001
7/7/2001
NaN NaN NaN
6)22/2000 NaN NaN
NaN NaN NaN
6)23)2000 6/27QOOO NaN
6/13)2000 6/16/2000 6/18)2000 6/20/2000
NaN NaN NaN
NaN NaN NaN
6/1 7)2000 6/20/2000 NaN
7/12)2000 NaN NaN
6/1 5/2000 NaN NaN
NaN NaN NaN
7/11/2001 NaN NaN
NaN NaN NaN NaN
7)2/2000 7)6)2000 NaN
7)6/2001 7/1 0/2001 NaN
5/21 Q001 5/23/2001 5/27/2001 5)31/2001
7/1 3)2000 7/1 7/2000 7)21 )2000
6/18/2001 6/22Q001 NaN
7/15/2000 7/17/2000 7/20/2000
5/23/2001 5)27/2001 NaN
6/16/2001 NaN NaN
NaN NaN NaN NaN
7/1CW2001 7/12)2001 NaN
Some final notes about data errors:
1) MCestimate will only look for errors in columns that you specify for analysis. It ignores other
columns. For example, had you omitted specifying ht as a covariate in the above example, no error
would have been generated for the missing value in the cell in row 12, column 4 (though nest 2 would
still have generated an error for an observation of less than 1 day). However the displayed nest file
would be unchanged (i.e., it would still look like Figs. 9 & 10).
2) Another possible error, having non-numeric data in a column specified for a quantitative covariate,
will crash MCestimate.
3.4 Re-describing the data after fixing errors
If you make changes to the data file in the NestFile window MCestimate will automatically try to parse
the data again, and if you haven't fixed the errors (or if you've created new ones!) then MCestimate will
display the same error again. You cannot perform any analyses until you successfully navigate the
import screens and get notification of a successful import (e.g., Fig. 6).
3.5 Opening a saved nest file
Once you've successfully described your data, the MCestimate window will display a file name under
Data file. The file has been saved to your hard drive and, in future sessions, can be opened directly in
MCestimate (without going through the import and describe data processes above). Or you can begin
analysis immediately. If you wish to use a previously imported data set choose Open nest file from the
File menu.
14
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3.6. Displaying summary information
If you have a nest file open that has been successfully parsed, then you can quickly view summary
information about the file by choosing Display summary info from the File menu. Doing so for the
imported data SimData.xls should look like Fig. 11.
Figure 11. The summary information screen for SimData.mat
,' SimData.mat
Source file = SirnData.
Number of subjects = 500.
Fledge = 211
depredated = 191
weather = 98
Number of observations = 1737.
Number of exposure days = 5113.
Effective sample size = 4538 days.
Beginning of first observation = 03-May.
End of last observation = 23-Jul.
Length of season = 83 days.
Duration (mean W- sd) of observations = 2.94 W- 0.32 days.
Number of categorical covariates = 2.
Number of quantitative covariates = 4.
Was information provided on age?: VE9.
3.7 Exporting a file for analysis in program MARK
You may wish to see whether you get the same answer in MCestimate that you get using program
MARK (White and Burnham 1999). For binomial fates the two programs should give virtually identical
results. I've tried to make this an easy comparison by adding the Export MARK file option. Choosing this
option will prompt you for a file name (say FileName), then create two files, FileName.inp and
FileName.txt. FileName.inp is an encounter history file formatted for immediate import into MARK.
FileName.txt gives you some supporting information, including the number of encounter occasions
(length of the nest season, defined from first active date to last nest-check) and the names of covariates
(if you specified any in the DescribeData GUI). You will need to input the season length value into the
Encounter occasions box in MARK. You may wish to add the covariate names under the Enter Ind. Cov.
Names option in MARK.
15
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4. Modeling nest failure
Analysis is done through the Analysis menu, which has five options (Fig. 12, Table 4).
Figure 12. The Analysis menu
.' MCestimate
d
r_
Design models
Load models from file
Load AIC table
Status
Ready.
c
LLoad model list
Manage lists
Fitted models:
Decimal precision: 2
Run models
Interrupt
Response Variable:
O Binomial (success/fail) 0 Multinomial
Pending model;:
Model name
Model name
AICc delta AICc Weight
Table 4. The Analysis menu
Menu Item
Description
Design models
Load models from file
Load AIC table
Load model list
Manage lists
Opens the ModelDesign window (Section 4.2 below).
Imports a list of models from Microsoft Excel (Section 4.3 below).
Opens a window for displaying previously saved results (Section 6 below).
Opens a window for adding a previously specified list of models to run (Section
6 below).
Opens a window displaying both previous results tables and model lists. This
choice is for deleting saved results (Section 6 below).
4.1 Specifying the response distribution
Before designing models for analysis you must specify whether you wish to analyze binomial or
multinomial responses. The default is multinomial. If your fate variable contained only two fates to
begin with then the two options will provide identical results. A note of caution! Changing the response
variable during analysis will delete the current pending models list and results table (you will get a
16
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warning first). This is to prevent you from inadvertently creating an AIC table comparing multinomial
and binomial models.
4.2 Overview: designing models
Primary analysis is done using the ModelDesign window, which is accessed using the Design models
option of the Analysis menu. With the ModelDesign window open (Fig. 13) you can design multiple
models and then run them from the main MCestimate window. The default model is the Intercept-only
model (no covariates, all failure rates temporally constant). MCestimate uses fairly conventional
notation to name models. Each failure rate is designated as a basic model parameter and is specified as
a function of specific covariates using parentheses. If no covariates are used then the parentheses
brackets contain only a dot - indicating that the basic parameter is assumed constant across all nests
and over time. This model, the intercept-only model, can be added to the list immediately by clicking
the button Add to pending models. In the example above this will add the model
weather(.)depredated(.) to the Model Set listbox.
Figure 13. The ModelDesign window for SimData.mat as created in Section 3.2
Response
Failure slates:
Model Name:
i.lfF.'rfiJ.-tfiJ r.|i.'eather(.)
Add 1o pending models Remove from pending models
Pending models:
*
v
Covariates:
yr c
it
hi
Age
| ^ |
« Remove
Main effects:
^^^™±
nter act ions:
J
Set interaction ]
Remove interaction
4.3 Building models by specifying covariates
Your specified covariates appear in the Covariates listbox of MCestimate. Note that there are two
covariates (Date and Age) in that box beyond what you specified in the DescribeData step. MCestimate
creates Date automatically and Age if an Age at first visit column is specified on the DescribeData GUI.
Fates may be modeled using different covariates. To specify which fate you are currently working on,
17
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click that fate in the Failure states listbox. This will set the title of the box below to: Predictors for fate:
[fate]. Any covariates you specify will always be for the currently selected fate.
The buttons for specifying a covariate to a fate change depending on whether you have selected a
categorical or a quantitative covariate. Fig. 13 shows the display for a categorical covariate. If you click
on a quantitative covariate in the Covariates listbox the display will look like Fig. 14. With the exception
of Date and Age all covariates are assumed to be nest specific (i.e., constant within nests).
Figure 14. The ModelDesign window when a quantitative covariate is selected.
Model Name:
Add to pending models
Remove from pending models
Pending models:
Covariates:
yr_c
trt
y^i
5ate
Age
v
I
Power » | 1
Log» ] e
\ | —
NegExp» ] e
« Remove
Main effects:
V
nteractions:
•
Set interaction
Remove interaction
4.3.1 Adding a categorical covariate
Categorical covariates may be added to a model by selecting them in the Covariates listbox and clicking
Add ».
4.3.2 Adding a quantitative covariate
Quantitative covariates may be added by selecting them in the Covariates listbox and clicking the button
corresponding to the desired transformation.
18
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Power transformations
To add a power of a quantitative covariate click Power». MCestimate applies the indicated power
transformation (edit box to the right of Power ») to the quantitative covariate at run-time. The default
is untransformed (power = 1). Any power may be entered. Note, however, that entering zero will
simply generate a second intercept. Multiple powers of a given covariate may be entered sequentially
(e.g., {height+heightA2...}, etc.).
Log transformations
Log transformations work in analogous fashion to the power transformations (described above). The
edit box is for entering the desired base. The default is the natural logarithm (e). With the exception of
e, only strictly positive numeric values can be entered in the base edit box. Another restriction is that
the base cannot be 1. I'd recommend sticking to the bases 2, e, and 10. MCestimate will not add an
arbitrary constant to zeros to allow log transformations. Instead, if you attempt to log-transform any
quantitative covariate that contains data that are not strictly positive, you will get an error message and
you will not be allowed to use the log transformation.
Negative exponential transformations
The NegExp transformation is intended to allow you to model thresholds in a quantitative covariate (i.e.,
a steep slope at small values but negligible additional effect at large values). The edit box is for entering
the desired base. The default is the natural logarithm (e). The same restrictions apply to the base as
with the log transformation. However, there is no restriction on the value of the covariate, except that
very large numbers will result in "inf" errors that will crash MCestimate.
The Date covariate
MCestimate uses the dates you entered for visits (VI - V10 in simulated data, Fig. 1) to generate an
ordinal design variable (always called Date) to enable you to model within-experiment temporal effects.
It is the numbered day within the year (i.e., where day 1 = 1 January). Date is a quantitative covariate
that varies within nests with every day of the season (whereas other quantitative covariates above are
assumed fixed for a given nest). Ordinal dates are assumed to be non-leap year. In creating Date
MCestimate removes the year (i.e., 2 July 2006 and 2 July 2007 would have the same ordinal date: 184).
If you want a year covariate you must add it as a separate column in your Excel file. You could then ask
whether the effect of date differs by year by specifying an interaction between the Date and year
covariates.
The Age covariate
If you specify an age at first visit column, MCestimate generates an ordinal Age covariate in the same
way that it generated Date. Thus, like Date, the Age covariate will change with every day within a nest.
19
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4.3.3 Interactions
Once you've added at least two covariates for a given fate to the Main effects listbox, you may specify
an interaction. This is done by selecting all covariates you wish to be in the interaction in the Main
effects listbox and clicking Set interaction. If you select more than two (say n) covariates then
MCestimate builds all lower level interactions when generating the n-way interaction. If you remove a
main effect that is specified in an interaction MCestimate will crash at run time.
4.3.4 Finalizing a model
To build models you move covariates from the Covariates listbox to the Main effects listbox using the
rules described above and specifying any desired interactions. As you do so, the Model Name box in the
Models frame will keep track of the covariates you are adding and removing. When you are satisfied
with the model for the current fate you can select another fate in the Failure states listbox and
continue. Once you have specified the model you wish for all fates, then you can add it to the set for
analysis by clicking the Add to pending models button in the Models frame. If you change your mind
after adding the model to the model set, then simply select it and click Remove from pending models.
After you select Add to pending models the ModelDesign window reverts to the opening state, with the
default model being the intercept model. Fig. 15 shows the ModelDesign window with five models
designed and ready for analysis.
Figure 15. Some models designed in the ModelDesign window
Model Name:
depredatedC.JweatherQ
| Add to pending models [
Pending models:
Remove (rom pending models
depredated!;.) weatherf.) A
depredatedi; .)weather(yr_c)
depredated(yr_c)weather(yi-_c)
depredded(1rt)weatJTer(yrc)^
H
Covariates:
yT_c
trt
it
Date
4ge
fl
|— Categorical
Add»
1
« Remove
Main effects:
A
v
Ferncve interaction
20
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4.4 Importing models from a file
Models may also be typed into Excel and then imported to MCestimate. As an example, the above
models have been typed into the file "ModelRunList.xIsx" (Fig. 16). To do so, Choose Load models from
file from the Analysis menu and navigate the desired file. The resulting models will be loaded into the
pending models window. In the model list file the fates may be listed in any order, however the syntax
must match exactly the syntax that MCestimate uses for building files. Any models that do not conform
to this syntax are ignored.
Figure 16. Example model list for import to MCestimate
» ModelRunList.xIsx - Microsoft Excel
Home Insert Page Layout
•^ j(, Calibri '111
LU ^ IB i nH^V7
Paste
3 bid H.l<3»~
Clipboard ^ Font
Review View Add-Ins W - =
Alignment
Number
A
Styles
Cells
Z -
Editing
M < > M Sheetl Sheet2 Sheets
Probably the easiest way to learn MCestimate model syntax is to build a few models using the model
builder (Section 4.3). Here are the basic rules. Main effects are listed by name (yr_c, trt, Date, etc.).
Additive models are indicated by separating main effects with a plus sign (+). Interactions are indicated
by separating main effects by an asterisk (*). Intercept-only models are indicated with a period (.).
Transformations of quantitative covariates are indicated differently, depending on the transformation.
Power transformations of quantitative covariates are indicated with a caret symbol, followed by
the desired power (e.g., DateA2). Log transformations differ depending on the desired base. If the
natural log is desired, then the "In" notation is used, whereas if any other base is desired, then the
notation logX(covariate) is used, where X is the base (e.g., loglO(Date)) indicates a common log of the
variable Date). Similarly, the negative exponential transformation notation differs depending on
whether the desired base is e or not. When the base is e, then the negative exponential transformation
is indicated as exp(-covariate). For example, a negative exponential transformation of the Date variable
is indicated as exp(-Date). However, if a different base is desired, the notation used is, for example,
baseA(-covariate). The resulting transformations can be combined into additive and interactive models
as described in the previous paragraph.
21
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4.5 Running the models
Once you've specified as many models as you wish, select Close to return to the main MCestimate
window. You might wish to build the models in Fig. 15 to verify that you will get the same results from
running MCestimate, and so you will be able to follow the results menus in the subsequent material.
Upon closing the ModelDesign window, the main MCestimate window should look like Fig. 17, with the
table of pending models appearing on the left of the window. To run the models click Run models. As
each model runs, it will be removed from the Pending models table to the Fitted models table, which is
a fairly typical AIC table. If you've specified too many models and want your computer back you can
click Interrupt to stop the analysis. As each model is added to the AIC table, the table is reordered
relative to the model with the lowest AIC value. The AIC values are corrected for sample size, where
sample size is defined as the sum of the number of known days survived and the number of failed
observations (Rotella et al. 2004).
Figure 17. The main MCestimate window with models ready to run
File Analysis About
Expiration date:
Status -
Ready
Decimal precision:
Run models
Interrupt
Response Variable: —
O Binomial (success/fail) © Multinomial
Pending models:
depredated(.)weather(.)
depredated(.)weather(yr_c)
depredated(yr_c)weather(yr_c)
depredated(trt)weather(yr_c)
5 |depredated(Date+yr_c)weatherO
Model name
Model name
NLL
AICc
delta AICc
Weight
4.6 The Pending models context menu
Before clicking Run models or while running is paused by clicking the Interrupt button, models can be
removed from the Pending models table using the pending models context menu. This menu is
accessed by selecting a cell in the Pending models table and right-clicking, which will bring up four
choices (Fig. 18). Choosing Clear pending models will delete all of the pending models from the table.
They cannot be recovered, except by going back to the DesignModels GUI and rebuilding them (or
reimporting from a file). Choosing Export model list to Excel will open a dialog box for saving the
Pending models list to an Excel file for later import. This might be useful, for example, if you wish to run
22
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the same set of models on a different data set. Choosing Save model list will first prompt you for a
name for the model list then save the list for later use (Section 6.2 below) to the same MCestimate file
in which your data are saved. This option may be removed in future editions as it is now redundant with
the ability to save model lists to a distinct Excel file. Finally, the Delete model choice will delete all
highlighted models in the Pending models table.
Figure 18. The Pending models context menu
> MCestimate
File Analysis About
Expiration date:
- Status -
Ready.
Fitted models:
Decimal precision:
Interrupt
Response Variable: —
0 Binomial (successrtail) <•} Multinomial
Pending models:
Model name
Jepiedateduweatherf.)
depredatedf ,)weather(yr_c)
depredated(yr_c)weather(yr_c)
depredated(trt)weamer(yr_c)
depredated(Date+yr_c)weather(.)
Mudel ri
delta AICc
Weight
Clear pending models
Export model list to Excel
Save model list
Delete model
23
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Figure 19. Models after they have been run
File Analysis About
- Expiration date' —
31-Dec-2014
Data file:
SimData.mat
Status -
Ready
Run models
Interrupt
Response Variable:
O Binomial (success/fail) 0 Multinomial
Pending models:
Model name
Decimal precision:
depredated(Dste*yr_c)weather(.)
depredated(trt)weather(yr_c)
depredated( -)weather(yr_c)
depredated(yr_c)weather(yr_c)
5 depredatedf ,)weather(.)
Model name
AICc
delta AIO:
Weight
962.01
968.77
970.46
970.23
973.72
1932.03 0
1945.54 13.51
1946.93 14.9
1948.47 16.44
1951.45 19.42
5. Interpreting model results
Once you've run the model, the output table (Fitted models) gives you the negative log-likelihood (NIL)
of the model, the corrected AIC value (AICC), the delta AICC value relative to the lowest AICC value in the
set, the model Weight (calculated following Burnham and Anderson 2002), and the number of
estimated parameters (K) for the model (Fig. 19). Models are sorted from lowest AICC to highest.
The results given in the Fitted models table are only a start. Much more information can be gleaned
using the context menu. To enable this menu you must select a row (any cell) in the Fitted models table
and then right-click your mouse. This will bring up a context menu with two choices Model (Table 4, Fig.
20) and Table (covered in Section 6, below). Most of these options are fairly self-explanatory and can be
understood by reading the descriptions in Tables 4 and 5. The Show parameter estimates window will
probably be the most useful and I describe this option at length below.
24
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Table 4. The Model context menu in the Fitted models table
Menu Item
Description
Rerun model
Show convergence stats
Show parameter estimates
Assess goodness of fit
Export estimates
Delete model
This reruns the model with a different (randomly chosen) starting point
for the numerical optimization.
This brings up a message box giving the convergence statistics for that
particular model.
This brings up a new window with each of the estimated parameters
(Figs. 20-22 below).
This brings up a new window that allows you to run a goodness-of-fit
test. I have just added four goodness-of-fit algorithms (see Section
5.3).
Exports the maximum likelihood parameter estimates, covariance
matrix and the predicted probabilities for each nest over the period of
observation (not over the life of the nest) to an Excel file.
Deletes the models selected in the Fitted models table.
Figure 20. The Model context menu
File Analysis About
Expiration date:
Status
Ready
Decimal precision:
Run models
Interrupt
- Response Variable: —
O Binomial (success/fail) 0 Multinomial
Pending models:
Model name
Model name
NIL
delta AICc
Weight
_ ted(trt)we; Bfc^JJ
jBJdepredatedQweat Table >
redated(yr_c)weather(yr_c
^Sjdepredatedf Jweather(.)
Rerun model
Show convergence stats
Show parameter estimates
Assess goodness of fit
Export estimates
1932.03
1945,54
194693
1948.47
1951.45
0
13.51
14.9
16.44
19.42
Delete Model
25
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5.1 Model convergence
Occasionally MCestimate will fail to converge on a solution. This is more likely to happen the greater
the dimensionality (number of parameters) of the model that is designed. Indicators of failed
convergence include NaN in the NIL column of the Fitted models table or multinomial logit scale
parameters that are equal to 10 (or minus 10), indicating that the optimization ran to a maximum
(minimum). The latter is most likely to occur when all nests share the same fate. In particular, if you
attempt to optimize a categorical covariate with many levels, it may occur by chance that all nests in
that category share the same fate, which may result in the optimization running to a boundary condition
(depending on what other covariates are in the model). If the optimization failed to converge due to a
poor starting point you may try re-optimizing it from a different starting point. To rerun a model, select
that model and chose model, rerun model in the Fitted models context menu. If you have reached a
boundary condition due to invariant fates in a given category this will not help. In the latter case, your
data do not provide sufficient information for estimation and you should not try to fit that model.
The convergence criteria for each model are also available as a MCestimate menu option. To see the
convergence statistics for a given model choose Show convergence stats under the model option in the
Fitted models context menu.
5.2 Parameter estimates
The most useful context menu choice is the Show parameter estimates choice under Models (Fig. 20),
which loads the Farms window (Fig. 21). In the Farms window, parameter estimates are given at three
scales (Multinomial logit scale, daily probabilities, and overall probabilities).
Figure 21. The Parms window
depredated(trt)weatherCyr_c)
rWK, — =. -
9
Fate Parameter Estimate 5E mfri max fit
1 depredated Intercept -3.3040 0.1076 1 1 1
3 weather Intercept -4.0861 0.1 484 1 1 1
* weather yr_c: 1 0 .5227 0 .2028 0 1 0
O Date calculator
z -value tor confidence intervals:! 1.96 ) decimal precision: I 4
1 Parameter MLE 5E L_CL U_CL
Jlsuccess 0.9492 0.0043 0.9365 0.9594
2 depredated 0.0349 0.0036 0.0283 0.0423
jTJweather o .01 60 0 .0023 0 .01 1 9 0 .021 4
i
start j 1~ ] days. enttf l| | days. decimal precision : 4
Outcome Estimate SE
1 hedge 0.9492 0.0043
2 depredated 0.0349 0.0036
3 jweather 0 .01 60 0 .0023
26
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5.2.1 Multinomial logit scale estimates
The logit scale estimates (the "betas") are difficult to convert into survival probabilities because the
probabilities depend not only on the betas, but also on particular covariate values. The fit column of the
first table shows which covariate values are used for fitting. When the Farms window is initially
opened, the fit column is set to 1 for all intercept parameters, 0 for all categorical covariate levels
(representing the reference category(s), which is lumped in with the intercept), and the mean value of a
covariate for all quantitative covariates. For interactions, the product of the fit values for each main
effect in the interaction is taken. These fit values are then used to generate the probabilities reported in
the Daily estimates table, which should contain one row for each fate (including success).
5.2.2 Daily Estimates
Daily survival and failure rates are reported in the Daily estimates table. This table has five columns and
as many rows as nest outcomes (including success). The column MLE gives the fitted probabilities
corresponding to the values of covariates in the fit column of the Multinomial logit scale estimates
table. Similarly the subsequent columns give the standard error of the fitted probability and lower and
upper confidence limits of the parameter. The standard error is calculated using the delta method
(Seber 1982). Confidence limits are calculated following the strategy outlined by Sambamoorthi et al.
(1999). They are symmetrical around the linear portion of the model (prior to transformation via the
multinomial logit) and become asymmetrical under the transformation. The z-value specifies the desired
nominal coverage of the confidence interval. The default is z = 1.96 corresponding to an approximate
95% confidence interval. Changes in the fit column of the Multinomial logit scale estimates table are
immediately applied to the Daily estimates and Overall estimates tables.
5.2.3 Overall Estimates
The third table, Overall estimates, extrapolates the daily probabilities for a single nest over the length of
a cycle defined by the entries in the start and end edit boxes. The extrapolation to overall rates is done
under the assumption that the particular covariate values in the fit column of the Multinomial logit
scale estimates table pertain to the nest at Age = 1 day. Overall estimates are calculated for the period
lasting from Age = start through Age = end, assuming the nest is still "alive" at age start. If you do not
specify an Age covariate, the actual values of start and end are irrelevant and all that matters is their
difference (the number of days for which an "Overall" estimate is desired). In this case you should
always specify Ifor start. The ability to specify start is designed to allow you to obtain "Overall"
estimates for a given developmental stage (e.g., the nestling phase). Temporal covariates (Age and
Date) are assumed to increment by 1 each day from start until end is reached. All other covariates are
assumed fixed for that particular nest.
5.2.4 Exploring the parameter space
Of course, the mean of quantitative covariates and the reference category of categorical covariates are
not necessarily the only portions of the covariate space of interest. Therefore the fit column in the first
table allows limited interaction. All main effect values can be edited. Intercept values and interactions
27
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cannot be edited. Intercepts must always be "1" and interactions will change with changes in the
corresponding main effects.
5.2.5 Design variables for quantitative covariates
All quantitative covariates are rescaled (by dividing by their standard deviation) when they are
converted to design variables. MCestimate retains the standard deviations in memory so that the
covariance matrix for untransformed variables can be estimated from the covariance matrix for the
transformed variables.
5.2.6 Design variables for categorical covariates
All categorical covariates are converted to indicator variables (columns of ones and zeros) indicating
whether a particular nest is in that category. Each categorical covariate with n levels generates n-1
indicator variables. The other category is lumped into the intercept. MCestimate arbitrarily allocates
the first level it encounters of any categorical covariate into the intercept. In the example above the
level "hi" of the categorical variable trt was lumped into the intercept.
5.2.7 Effects of changing covariate values on other covariates in the model
In some cases, changing a covariate value in the fit column will automatically change the value of other
covariates in the model. When a level of a categorical covariate is set to "1" all other levels of that
covariate are set to zero (except the intercept). When a main effect fit value is changed, any interactions
involving that main effect will use the new value of that covariate, so the interaction values will change
also. Similarly, when multiple powers (or other transformations) of a quantitative covariate are
simultaneously included in a model, changing the fit value for one transformation will result in a
corresponding change to the fit values of the other (i.e., if "variable" is set to "3" then "variableA2" will
automatically change to "9" and vice versa).
Example 1. Interpreting parameter estimates
To get a sense for how to use the Farms window, click on a cell in the second row of the output table on
the main MCestimate window (i.e., highlighting the model: depredated(trt)weather(yr(c))), which is
the model hypothesizing that the nest-predation rate depends on treatment (a categorical covariate)
and that the weather-related failure rate depends on year (a categorical covariate). Then right-click and
choose Model > Show parameter estimates. The Farms window should look like Fig. 21 (above).
Suppose you were interested in the predation rate under the treatment condition lo. Then click that cell
(row 2, column 7) in the fit column, type "1" and hit the "Enter" key . The new Farms window should
look like Fig. 22. Note the changes in daily and overall parameters that have occurred in the second
table (compare Fig. 21 to Fig. 22).
28
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Figure 22. Parms window from Fig. 21 with trt:lo set to "1"
— Model name
depredsrted(trt)weather(yrj;)
Multinomial loglt scale estimates: -
Fate | Parameter
depredated Intercept
depredated iitlo
weather Intercept
weather yr_c:1
-3.3040
0.2727
-4.0861
0.5227
0.1087
0.1474
01541
0.2087
O Date calculator
Daily estimate?.
z-value for eonSctenoe Hwvats: 1.96
| Parameter
1 [success
2 depredated
MLE SE LJO.
0.9389 0.0049 0.9247
0.0453 0.0043 0.0373
0.0158 00024 0.0116
U_CL
0.9505
0.0548
0.0214
- Overall estimates: —
start:[ 1 i days.
Outcome
1 JFIedge
2 depredated
3 [weather
i Estimate
0.9389
0.0453
0.0158
5E
0.0049
0.0043
0.0024
In Fig. 22, above, the overall rates are equal to the daily estimates because the start and end edit boxes
are set to 1. Setting these values to 1 and 25, respectively (i.e., a 25-day nest cycle, from first egg to
fledging) should give you the result displayed in Fig. 23.
Figure 23. Parameter estimates from Example 1 for a 25-day nest cycle
Model name
depredated(trt)weather(yr_c)
Fate | Parameter i Estimate 5E min max fit
1 depredated Intercept -3.3040 0.1076 1 1 1
2 depredated trtlo 0.2727 0.1463 0 1 1HHKI
3 weather Intercept -4.0861 0.1484 1 1 1
4 weather yr_c:1 0.5227 0.2028 0 1 0
O Date calculator
z-value for confidence intervals:]"! ,95 | decimal precision: | 4
Parameter MLE SE L_CL U_CL
_Msuccess 0.9389 0.0048 0.9251 0.9502
_2_idepredated 0.0453 0.0042 0.0375 0.0546
3 jweather 0.01 58 0.0023 0.01 1 7 0.021 2
1
!tat| 1 days. end: 25 days. decimal precision: | 4
Outcome Estimate SE
1 Fledge 0.2068 0.0267
2 depredated 0.5883 0.0340
3 [weather 0.2049 0.0267
29
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Example 2. Interpreting parameter estimates when Date is included
Close the Parms window and go back to the main MCestimate screen. Choose the "best" model
(depredated(Date+yr)weather(.)) and display its parameter estimates. The numbers in the min, max,
and fit columns for the Date covariate are not easily interpreted because they are ordinal dates. The
Date calculator allows conversion between calendar dates and ordinal dates (and their
transformations). It can be displayed by clicking the Date calculator radio button below the
Multinomial logit scale estimates table (Fig. 24). Typing "167" into the Ordinal: edit box should result in
"15-Jun" appearing in the Date (dd-mmm): edit box. If you've used a transformation of Date you can
also accommodate for it using the appropriate controls to the right and the transformed design variable
will be displayed (on its native scale, not divided by its standard deviation). Changes to any of the three
edit boxes (Date (dd-mmm):, Ordinal:, or Design variable:) will carry through to the other two. Note
that this calculator cannot currently handle negative exponential transformations.
Figure 24. Using the Date calculator to interpret models with "Date" as a covariate
depredated(Date+yr_c)weather(.)
Fate Parameter Estimate
3 depredated yr_c:1 0.0798
•* weather Intercept -3.8314
Date (dd-mmm): O
® Date calculator
SE min max fit
0.1438 0 1 0
0-1023 1 1 1
dinai: Design variable: ® Power transformation power;
J L 1 J U °9 ansor n | 1
;
i-value for confidence intervals: 1 .96 decimal precision: 4
Parameter MLE SE L CL U CL
_J_|success 0.9431 0.0040 0.9314 0.9529
2 (depredated 0.0365 0.0036 0.0300 0.0443
3 jweather 0.0204 0-0020 0.01 67 0.0250
1ait| 1 jdays, end: 1 days. decimal precision: | 4
Outcome Estimate 5E
_1_ Fledge 05431 0.0040
2 depredated 0.0365 0.0036
3 weather 0.0204 D.0020
5.3 Goodness-of-fit
Assessing the fit of nest survival models is challenging (Sturdivant et al. 2007). MCestimate uses several
different algorithms, including a multinomial extension of the Hosmer-Lemeshow test (Hosmer &
Lemeshow 2000), a similar method described by Pigeon and Heyse (1999), and two methods based on
30
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parametric bootstrap (White et al. 2001). The latter algorithms rely on repeatedly generating sets of
data from the maximum likelihood estimates of the linear coefficients and fitting the same model to the
new sets of data. In this way, a null distribution of a given test statistic is generated under the
hypothesis that the data arose from the fitted model parameterized with the estimated MLEs. The
complement of the proportional rank of the test statistic is taken to be the p-value for that test statistic.
Several test statistics are available for use in the parametric bootstrap procedure, including the deviance
from a saturated model (Deviance) and various forms of the power-divergence family of statistics (Read
& Cressie 1988). The latter family includes the Pearson X2 statistic and the Freeman-Tukey statistic. I
recommend that you use the parametric bootstrap option with caution! It is very slow and often does
not exhibit improved performance compared to the Hosmer-Lemeshow and Pigeon-Heyse tests, which
are assessed against chi-square distributions with known degrees of freedom (hence do not require
lengthy simulations).
To use these algorithms choose Assess goodness of fit under the model option in the Fitted models
context menu (Table 4). This will load the GoF GUI (Fig. 25).
Figure 25. The GoF GUI when first loaded
depredated(Date+y rjiOweatheri;.)
Groups:
1 Test Statistic
Hosmer-Lemeshow 14 4505
Pigeon-Heyse 14.4704
I
dr Prob
18 0.6993
13 0.6980
Power diver yen.? :t
View contributions lambda: I 1
Run
1
2
3
Fate
Interrupt
Parameter
Estimate
Continue
— Iterations: —
| 100 |
SE (hessian) SE (bootstrap)
1
o.e
0.6
0.4
0.2
°[
Status:
Current deration: Overdispersion (c hat):
Observed Current Value Probability
10 20 30 40 50 60 70 80 90 10C
At the top of the GoF GUI the name of the model to which the current goodness-of-fit results pertain is
displayed. Immediately below the model name is a panel (Goodness-of-fit based on grouping
strategies) showing p-values for the Hosmer-Lemeshow test and the Pigeon-Heyse test. The default
value for the number of groups to consider is 10 (following guidance from Hosmer and Lemeshow 2000),
but you may enter other values. Typically the Hosmer-Lemeshow p-value is very close to that for the
31
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Pigeon-Heyse statistic given the same number of groups. Below these results is the Parametric
Bootstrap panel. To run a parametric bootstrap test you must choose how many iterations you wish to
simulate and click Run. Usually 100 iterations is enough to figure out whether you should be concerned
about goodness-of-fit, but if so, then you should run at least 500 iterations (better yet 1,000). Plan on
having something else to do during that time! Above and to the right of the Parametric Bootstrap panel
is a small panel labeled Power divergence statistic. This box has two uses. First, the parameter lambda
determines which member of the Power divergence family is used as the test statistic in the Parametric
bootstrap. A value of lambda = 1 corresponds to Pearson's X2 statistic. A value of lambda = -0.5
corresponds to the Freeman-Tukey statistic. Reed and Cressie (1988) recommend a value of lambda ~
%. You don't necessarily need to decide in advance because you can change the value of lambda on the
fly (example below). The ability to change the value of lambda is intended to allow you to ensure that
your data do not exhibit lack-of-fit under different statistics. It is NOT intended to allow you to shop for
a statistic under which you get an acceptable p-value! The second use for the Power divergence statistic
panel is to allow you to view the contributions from each particular observation in your data set to the
Power divergence statistic (with parameter lambda). To do so, enter the desired value of lambda and
choose View contributions. This will bring up a table of contributions (described in example below).
If you run a parametric bootstrap test, in addition to the chosen power divergence statistic, you will also
be provided with goodness-of-fit results for the deviance of the current model compared to a saturated
model. You will also generate estimates of overdispersion and bootstrap estimates of the standard
errors of the linear coefficients. Do not be too alarmed if these disagree with the estimates generated
from the Hessian matrix. It can take many iterations for the bootstrap estimates to converge. However,
if after many iterations the estimates still do not agree, then the bootstrap estimates are probably more
reliable, especially at small sample sizes. Finally, the parametric bootstrap test will also generate a
graphical display showing the current value and cumulative probability trajectory of the goodness-of-fit
statistics. This is intended to help you decide when enough simulations have been run.
5.4 Example. Assessing Goodness-of-fit
If you have imported SimData.xls as described above and fitted the Models from Section 4, then load the
GoF GUI so that it looks like Fig. 25. Preliminary indications from the Hosmer-Lemeshow and Pigeon-
Heyse tests suggest little evidence for lack-of-fit (Fig. 25). For further verification, a bootstrap goodness-
of-fit test could be run. To do so, simply click Run within the Parametric Bootstrap panel. Fig. 26 shows
the bootstrap results after 100 iterations (note this took about 30 minutes to generate).
32
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Figure 26. Bootstrap goodness-of-fit results for the depredated(Date+Yr_c)weather(.) model
depredated(Date+yr_c)weatherC.)
Groups:
Hosmer-Lemeshow
Pigeon-Heyse
Test Statistic c
144505
14.4704
f Prob
18 0.6993
18 0.6980
Power divergence statistic -
View contributions
, 1
Parametric Bootstrap
depredated
weather
r Iterations: —
Interrupt Continue | I — I
Parameter Estimate SE (hessian) SE (bootstrap)
d Intercept -0.0156 0.6632 0.6816
d Date -0.0193 0.0040 0.0338
Intercept -3.8314 0.0991 0.1039
1
O.B
0.6
04
3atus:
Current iteration: 1 Overdispersion (c_hat):
Observed Current Value Probability
Deviance 1924 1816 0.23
\Vvs_
0.2
10 20 30 40 50 BO 70 BO 90 10c|
According to the table showing goodness-of-fit statistics (above the panel graph of probabilities), the
observed deviance (compared to a saturated model) was 1,924, which was well within the distribution
of simulated deviances (Fig. 26). However, the Pearson X2 statistic was higher than almost all simulated
values, indicating lack-of-fit. The probability is 0.02 in this case because the observed value of X2 from
the empirical data is taken to be the first member of the simulation set and one iteration of the
simulation (around iteration 16) produced a value of X2 greater than the observed value. Thus 2 out of
100 values were greater than or equal to the observed value. To see which observations are
contributing the most to the test statistic, you can click View contributions in the Power divergence
statistic panel. Doing so in this case, with lambda=l, should produce a table looking like Fig. 27.
33
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Figure 27. Table of observation-specific contributions to the Peason X2 statistic
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
1234
Nest Date Length Outcome
39 17-May-2QOO 2 weather
201 1 8-May-2000 2 weather
105 23-May-20QO 2 weather
166 28-May-2QOO 2 weather
450 27-May-2000 2 weather
S4 Q2-Jun-200Q 2 weather
375 Q5-Jun-200Q 2 weather
241 06-Jun-2000 2 weather
142 Q3-Jun-2QOO 2 weather
362 Q8-Jun-20QQ 2 weather
127 09-Jun-2000 2 weather
41 Q5-Jun-200Q 2 weather
337 1Q-Jun-200Q 2 weather
349 13-Jun-2000 2 weather
3S1 21 -Jun-2000 2 weather
230 22- Jun-2000 2 weather
260 23-Jun-2000 2 weather
361 23-Jun-200Q 2 weather
369 26- Jun-2000 2 weather
130 29-Jun-2000 2 weather
231 25-Jun-2000 2 weather
186 07-Jul-2000 2 weather
250 04-JUI-2000 2 weather
442 04-Jul-2000 2 weather
183 15-Jul-200Q 2 weather
399 1 1 -Jul-2000 2 weather
455 11 -Jul-2000 2 weather
49 18-Jul-2000 2 weather
44 22-JUI-2000 2 weather
126 07-Jul-2000 2 depredated
100 06-Jul-2000 2 depredated
400 06-JUI-2000 2 depredated
412 06-Jul-2000 2 depredated
224 01 -Jul-2000 2 depredated
5 6
survived depredated
0.3333 0.12S9
03440 01173
0.3457 0.1161
0.3552 0.1063
03607 01005
0.3639 0.0972
0.3688 0.0922
0 3704 0 0905
0.3722 0.0887
0.3735 0.0873
0 37SO 0 0853
0.3752 0.0855
0.3765 0.0842
0 3864 0 0740
0.3912 0.0690
0.3924 0.0677
0 3936 0 0665
0.3936 0.0665
0.3971 0.0629
0 9003 0 0593
0.9005 0.0594
0.9083 0.0514
0 9093 0 0503
0.9093 0.0503
0.9151 0.0443
09152 00442
0.9152 0.0442
0.9175 0.0419
0 9204 0 0389
0.9119 0.047S
0.9111 0.0485
09111 00485
0.9073 0.0523
0.9065 0.0532
7
weather
0.0378
0.0382
0.03S3
0.0386
0.0388
0.03S9
0.0390
0.0391
0.0391
0.0392
0.0392
0.0392
0.0393
0.0396
0.0398
0.0398
0.0399
0.0399
0.0400
0.0401
0.0401
0.0403
0.0404
0.0404
0.0406
0.0406
0.0406
0.0407
0.0407
0.0405
0.0404
0.0404
0.0403
0.0403
8
PDS contrib.
25.4264
25.1777
25.1 385
24.9231
24.7934
24.7279
24.6197
24.5850
24.5463
24.5176
24.4848
24.4B03
24.4528
24.2410
24.1 382
24.1128
24.0879
24.0B79
24.0161
23.9433
23.9453
23.7859
23.7847
23.7647
23.6468
23.6446
23.6446
23.6000
23.5416
20.0134
19.6266
19.6266
1 8.1 029
17.8008
As you can quickly determine by inspection, the greatest contributions to the Peason X2 statistic in this
case are coming from observations on weather failure. Scrolling further down (not shown) you would
find that the next largest contributions come from observations on predation events, followed by
observations over which nests survived. This is typical, as the occurrence of rare events will dominate
the Pearson X2 statistic when all cells have exactly one observation (hence the need to evaluate the
distribution of the test statistic via parametric bootstrap).
Changing the value of lambda in the Power divergence statistic panel will change the test statistic and
will retroactively apply the changes to the results of the Parametric Bootstrap. For example, the next
figure shows the results for the Freeman-Tukey statistic (Fig. 28).
34
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Figure 28. Parametric bootstrap results for the Freeman-Tukey statistic
OWE
depredated (Date+yr_c)weatherO
Groups:
Hosrner-Lemeshow
Pigeon-Heyse
Test Statistic c
14.4505
14.4704
f Prob
13 0.6993
18 0.6980
Power divergence statistic -
View contributions lambda: I -°-5l
— Parametric Bootstrap
Fate
depredated
depredated
weather
Interrupt
Parameter
d Intercept
d Date
d yr_c:1
Intercept
Estimate
Continue
SE(hessian) SE(b
-0.0156 0.6632
-0.0193 0.0040
0.0798 0.1487
-3.8314 0.0991
,— Iterations: —
100
ootstrap)
0.661 6
0.0338
0.1564
0.1039
— Status: —
Current deration: 100 Overdispersion (c_hat):
Observed Curren
Deviance 1924 1318
Freernan-Tukey 2596.6 24543
t Value Probability
0.23
0.4
- Freeman-Tukey
10 20 30 40 50 60 70 BO 90 100
Unlike the Pearson X2 statistic, the Freeman-Tukey statistic does not suggest lack-of-fit (Fig. 28). This
should be interpreted with caution! Limited power analyses suggest that the Freeman-Tukey statistic
rarely has much power to detect lack-of-fit (for these kinds of data) and that the Pearson X2 statistic
tends to reject at the nominal rate when the model fits the data. Thus I do not recommend adoption of
the Freeman-Tukey statistic without good a priori justification. Fig. 28 also shows that by 100 iterations,
the bootstrap estimates of standard errors are fairly close to those obtained from the Hessian (with the
exception of the estimate for Date). This happened fairly rapidly in this case and you should not expect
such rapid agreement! Finally, note also that overdispersion is small (c —1.0223) and can probably be
ignored.
5.5 Exporting MCestimate results
All tables in MCestimate can be copied and pasted into other programs. To do so, select the cells you
wish to copy and press ctrl-c to copy the cells into the windows buffer. They can then be pasted using
ctrl-v or the edit-paste menus of most programs.
MCestimate provides two additional ways to export results. The first is Export estimates under the
Model choice of the Fitted models context menu. Choosing this option will bring up a file save dialog
35
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(Fig. 29) with a default name being the name of the model under which the estimates are derived
(though you may change it).
Figure 29. The file save dialog that appears after choosing Export estimates.
> Output file
nlfx
Provide a file name:
|pepredated(Date+yr(c))we9l
OK Can
EZH
;el
This option saves an Excel workbook with three worksheets. Sheetl will contain the MLEs (the betas)
and the covariance matrix. SheetZ will contain fitted probabilities for each nest from the time of
discovery to the end of monitoring (note these are not fitted probabilities over the life of the nest!).
Sheets will contain fitted probabilities for each observation on each nest. I recommend caution
interpreting the values on SheetZ and Sheets. They are generally equivalent to neither daily nor overall
values. This option is included to facilitate a do-it-yourself goodness-of-fit test.
Another way to export results from MCestimate is to use the File menu on the Farms GUI (e.g., Fig. 22,
above). To use this function you must first select the name of a quantitative covariate in the
Multinomial logit scale estimates window. MCestimate will then generate 101 values of the selected
quantitative covariate evenly spaced between the minimum and maximum value of the covariate. It
then uses those 101 values to fit daily and overall probabilities as described above (Sections 5.2.2 and
5.2.3). The resulting fitted probabilities are exported to an Excel file of the same name as the selected
covariate (in this case Date.xls, Fig. 25). This function is intended to help with graphing the relationship
between the fitted probabilities and continuous covariates.
36
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Figure 30. A portion of the file Date.xls, sheet = weather,created using the Export series button
a
Paste
J ">-
'
Cahb
-J Copy
J Format Painter B
IVbo.ra
Ai
I A j B
1 [Dale Idaily est.
2 124 0.0194
3 124.81 0.0194
4 125.62 0.0194
5 126.43 0.0194
6 127.24 0.0195
7 128.05 0.0195
8 128.86 0.0195
9 129.67 0.0195
10 130.48 0.0196
11 131.29 0.0196
12 132.1 0.0196
13 132.91 0.0196
14 133.72 0.0197
15 134.53 0.0197
16 135.34 0.0197
17 136.15 0.0197
IS 136.96 0.0197
19 137.77 0.0198
20 138.58 0.0198
21 139.39 0.0198
22 140.2 0.0198
23 141.01 0.0199
24 141.82 0.0199
25 142.63 0.0199
26 143.44 0.0199
-
C
| •" - 1 A" »' ' — " s
Font l".
f. Date
D E F S
dailySELCI UCI overall est. overall SE
0.0020 0.0159 0.0236 0.0194 0.0020
0.0020 0.0159 0.0236 0.0194 0.0020
0.0020 0.0159 0.0237 0.0194 0.0020
0.0020 0.0160 0.0237 0.0194 0.0020
0.0020 0.0160 0.0237 0.0195 0.0020
0.0020 0.0160 0.0237 0.0195 0.0020
0.0020 0.0160 0.0238 0.0195 0.0020
0.0020 0.0160 0.0238 0.0195 0.0020
0.0020 0.0161 0.0238 0.0196 0.0020
0.0020 0.0161 0.0239 0.0196 0.0020
0.0020 0.0161 0.0239 0.0196 0.0020
0.0020 0.0161 0.0239 0.0196 0.0020
0.0020 0.0161 0.0239 0.0197 0.0020
0.0020 0.0162 0.0240 0.0197 0.0020
0.0020 0.0162 0.0240 0.0197 0.0020
0.0020 0.0162 0.0240 0.0197 0.0020
0.0020 0.0162 0.0241 0.0197 0.0020
0.0020 0.0162 0.0241 0.019S 0.0020
0.0020 0.0162 0.0241 0.0198 0.0020
0.0020 0.0163 0.0241 0.0198 0.0020
0.0020 0.0163 0.0242 0.0198 0.0020
0.0020 0.0163 0.0242 0.0199 0.0020
0.0020 0.0163 0.0242 0.0199 0.0020
0.0020 0.0163 0.0242 0.0199 0.0020
0.0020 0.0163 0.0242 0.0199 0.0020
«
a
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5.6 Visualizing MCestimate results
The File menu on the Parms window also contains the option Plot series. As above, to use this function
you must first select the name of a quantitative covariate in the Multinomial logit scale estimates
window. MCestimate will then generate 101 values of the selected quantitative covariate, as described
above and plot them for you with confidence intervals (the latter using specified z-values). For example,
with the Parms window open for the model depredated(Date+Yr(c))weather(.) and the name Date
highlighted in the Multinomial logit scale estimates table, choosing File/Plot series will produce three
figures that resemble Figs. 31-33, respectively.
Figure 31. Daily survival rate, with Date in the depredated(Date+Yr(c))weather(.) model
130 140 150
37
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Figure 32. Daily depredation rate, with Date in the depredated(Date+Yr(c))weather(.) model
7r riff
i
Figure 33. Daily rate of failure due to adverse weather, with Date in the
depredated(Date+Yr(c))weather(.) model
11
! J
. 0022
190 200 210
I would welcome suggestions and thoughts on how to improve these graphing functions!
6. Managing results tables and model lists
Constantly clicking through the creation of models in MCestimate can be tedious. Thus model lists and
AIC tables can be saved, re-opened, and subsequently modified (add or remove models). The easiest
way to do this is through the Table options in the context menu of the Fitted models table (Table 5, Fig.
34).
Table 5. The Table context menu in the Fitted models table
Menu Item
Description
Save AIC Table
Save as model list
Clear AIC Table
Saves the AIC table so that it can be loaded later. Saved AIC tables are
automatically saved to the data file currently in use.
Saves the models in the AIC table as a list that can be loaded and run at a
later time. Saved model lists are automatically saved to the data file
currently in use.
Deletes the Fitted models table. It cannot be recovered.
38
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Figure 34. The Table context menu
File Analysis About
Expiration date; -
Ready
Decimal precision:
Run models
Interrupt
Response Variable: —
O Binomial (success/fail) <•;• Multinomial
Pending models:
Model name
AICc
delta AICc
Weight
2 |depredated(trt)weather(yr j
jjdepredated( .)weather(yr_c; |
t depredated(yr_c)weather(yr_c)
5 ldecredated(.)weather(.)
962.01
QRR77
Save AIC Table
Save as model list
1932.03 0
1945.54 13.51
1946.93 14.9
1948.47 16.44
1951.45 19.42
Clear AIC Table
6.1 Saving an AIC Table
Choosing Save AIC Table under the Table option in the Fitted models context menu (Fig. 34) will load a
dialog box for specifying a name for the AIC Table. Note: spaces are not allowed in the table name. If
you include a space, the table will be saved, but will generate an error when you attempt to load the
table subsequently. Names of AIC Tables and model lists (below) should always begin with a letter.
When you save an AIC table, MCestimate automatically saves it to the current data file on disk.
6.2. Saving a model list
In some cases you may wish to save a model list to run in the future. This can be done in two ways. An
existing AIC table can be saved as a model list by choosing Save as model list under the Table option in
the Fitted models context menu. As with saving an AIC table, this will bring up a dialog asking you to
name the model list. Also as above, the name cannot include spaces. The second way to save a model
list is to choose Save model list in the Pending models context menu.
6.3 Managing lists
Once you've saved an AIC table or a model list it can be subsequently loaded under the Analysis menu
using the analogous load command (Load AIC table or Load model list). In either case, the choices you
will be offered to load will depend on the response variable that is currently selected in the radio button
on the main MCestimate page. MCestimate will only allow you to load model lists or AIC results that
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match the selected response variable (binomial or multinomial). As you save model lists and AIC tables
you may wish to delete lists that are no longer needed. You can do so under the Analysis menu choice
Manage lists. Saved model lists and AIC tables may be compiled into larger lists by loading them into
the main MCestimate window. Whenever you load a list or an AIC table you have the option of either
appending or replacing the existing table.
Acknowledgments
Thanks to T. Johnson, University of Wyoming (first MCestimate beta tester!) for suggesting some great
changes to the program and user's guide. Thanks also Allyson Jackson of Biodiversity Research Institute,
for using MCestimate to analyze Carolina Wren data and making many good suggestions for model
improvements. Finally, thanks to R. Greenberg of the Smithsonian Migratory Bird Center for patiently
waiting for ten years for this two-year project to finish. A. Kuhn and M. Starus provided valuable
editorial comments on this guide.
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