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Bootstrap Data


The simulation procedure in MARK now allows bootstrapping the encounter histories data to generate bootstrap replication.  To bootstrap encounter histories, you select the Bootstrap Data option from the Simulation menu choices.  Note that bootstrapping data is different than the bootstrap goodness-of-fit procedure

WARNING: An issue that you need to understand to use this procedure is that the encounter history file should be set up to have each history represent the appropriate number of animals.  Typically, this would be 1 animal, but as the example below shows, such may not be the case.  In general, encounter history files with encounter histories pooled so that the count frequency is >1 will not be appropriate to use in this procedure.  However, multiple identical encounter histories within 1 block can be combined as the example below shows.  Also, be careful about the group structure of your data -- encounter histories within groups are resampled, never across groups.

You should understand that the boostrapping of individual encounter histories will not provide any additional information from the usual analyses.  That is, resampling individual encounter histories generates the same estimates and standard errors as the usual analysis.  Where bootstrapping the encounter histories is most useful is when there are dependencies across animals.  The most typical example of such data are marking of young that are known to be siblings.  So, all the young in a litter are marked, or all the young in a nest are marked.  When the encounters of these animals are treated as if they are independent, the estimates will be generally unbiased, but the standard errors will be too small.  The reason for the standard errors being too small is that the sampling unit is really the litter or nest, and not the individual animal.  So, the sample size is assumed to be larger than it really should be.

To bootstrap litter or nest data such as described above, include an individual covariate that defines the nest or litter.  This variable can be continuous, such as nest number 1 to the number of nests, or litter number.  This covariate is then used to bootstrap the encounter histories, such that the nests or litters are resampled, instead of the individual encounter histories.

To run the data bootstrap, select the Bootstrap Data menu choice from the Simulation menu in the Results Browser, and then provide the information requested in the 3 tab windows:  1 or more models to estimate (Estimation Models),  the parameters of the simulation (Simulation Specification) that you want to save in the simulation results database, and the individual covariate to use for the bootstrap resampling.

Once you have created a simulation output file with the bootstrap samples and resulting estimates, you can view the results with the View Simulation Results menu choice.

The bootstrap data procedure only works with encounter history files containing encounter histories, and will not work with the summary input that is allowed for band recovery data or known fate data.  You have to convert these formats to the corresponding encounter histories.  One trick to do this is to use the residuals output file in Notepad, where the data are given as encounter histories.

One issue that users of the bootstrap data procedure should be aware of is how the frequency counts for encounter histories are handled.  These values are maintained with the encounter history, so are not changed by the bootstrap procedure.  So, if for some reason you want to bootstrap individual encounter histories, you may want to specify each animal separately, with a frequency of 1.  With the use of the individual covariate to specify the resampling structure, the frequencies can be >1 and make perfect sense.  As an example, consider an input file for known fate data with 1 occasion.  An individual covariate of Litter is also included in the encounter histories file.  

11  1 1;
10  2 1;
11  2 2;
10  2 2;
11  1 3;
10  3 4;

The above input file shows 4 litters of size 3, 4, 1, and 3, respectively.  For this reason, the count frequency for each encounter history can exceed 1, because the litter identifier provides the blocking to bootstrap the encounter histories.  Bootstrapping would be performed by resampling from the 4 litters if the Litter individual covariate was specified in the Bootstrap Data tab window.

Groups are kept separate in the bootstrap resampling process.  Thus, the number of litters is kept constant for each group in the resampled data.  Even though your model being estimated might ignore or combine groups, the bootstrap resampling will not ignore these groups.  The number of unique blocks of histories within each group will be sampled within that group, and never across attribute groups.  Also, for mult-state data, the bootstrap resampler does not distinguish between initial states, so that the conditioning on number of animals starting in each state is lost.