model.average.marklist: Compute model averaged estimates of real parameters

Description

Computes model averaged estimates and standard errors of real parameters for a list of models with a model.table constructed from collect.models. It can also optionally compute the var-cov matrix of the averaged parameters and their confidence intervals by transforming with the link functions, setting normal confidence intervals on the transformed values and then back-transforming for the real estimates.

Usage

## S3 method for class 'marklist':
model.average(x, parameter, data, vcv,
    drop=TRUE, indices=NULL, revised=TRUE,...)

Arguments

a list of mark model results and a model.table constructed by collect.models

parameter

name of model parameter (e.g., "Phi" for CJS models); if left NULL all real parameters are averaged

data

dataframe with covariate values that are averaged for estimates

vcv

logical; if TRUE then the var-cov matrix and confidence intervals are computed

drop

if TRUE, models with any non-positive variance for betas are dropped

indices

a vector of parameter indices from the all-different PIM formulation of the parameter estimates that should be presented. This argument only works if the parameter argument = NULL. The primary purpose of the argument is to trim the list of p

revised

if TRUE, uses revised variance formula (eq 6.12 from Burnham and Anderson) for model averaged estimates and eq 6.11 when FALSE

...

additional arguments passed to specific functions

Value

If vcv=FALSE, the return value is a dataframe of model averaged estimates and standard errors for a particular type of real parameter (e.g., Phi). The design data are appended to the dataframe to enable subsettting of the estimates based on features of the design data such as age, time, cohort and grouping variables. If vcv=TRUE, confidence interval (lcl,ucl) limits are added to the dataframe which is contained in a list with the var-cov matrix.

Details

If there are any models in the model.list which do not have any output or results they are dropped. If any have non-positive variances for the betas and drop=TRUE, then the model is reported and dropped from the model averaging. The weights are renormalized for the remaining models that are not dropped before they are averaged. If parameter=NULL, all real parameters are model averaged but the design data is not copied over because it can vary by the type of parameter. It is only necessary to model average all parameters at once to get covariances of model averaged parameters of differing types. If data=NULL, the average covariate values are used for any models using covariates. Note that this will only work with models created after v1.5.0 such that average covariate values are stored in each model object.

References

Burnham, K. P. and D. R. Anderson. 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Second edition. Springer, New York.

Examples

Run this code

data(dipper)
run.dipper=function()
{
#
# Process data
#
dipper.processed=process.data(dipper,groups=("sex"))
#
# Create default design data
#
dipper.ddl=make.design.data(dipper.processed)
#
# Add Flood covariates for Phi and p that have different values
#
dipper.ddl$Phi$Flood=0
dipper.ddl$Phi$Flood[dipper.ddl$Phi$time==2 | dipper.ddl$Phi$time==3]=1
dipper.ddl$p$Flood=0
dipper.ddl$p$Flood[dipper.ddl$p$time==3]=1
#
#  Define range of models for Phi
#
Phi.dot=list(formula=~1)
Phi.time=list(formula=~time)
Phi.sex=list(formula=~sex)
Phi.sextime=list(formula=~sex+time)
Phi.sex.time=list(formula=~sex*time)
Phi.Flood=list(formula=~Flood)
#
#  Define range of models for p
#
p.dot=list(formula=~1)
p.time=list(formula=~time)
p.sex=list(formula=~sex)
p.sextime=list(formula=~sex+time)
p.sex.time=list(formula=~sex*time)
p.Flood=list(formula=~Flood)
#
# Collect pairings of models
#
cml=create.model.list("CJS")
#
# Run and return the list of models
#
return(mark.wrapper(cml,data=dipper.processed,ddl=dipper.ddl))
}
dipper.results=run.dipper()
Phi.estimates=model.average(dipper.results,"Phi",vcv=TRUE)
p.estimates=model.average(dipper.results,"p",vcv=TRUE)
run.dipper=function()
{
data(dipper)
dipper$nsex=as.numeric(dipper$sex)-1
#NOTE:  This generates random valules for the weights so the answers using
#  ~weight will vary
dipper$weight=rnorm(294)
mod1=mark(dipper,groups="sex",
  model.parameters=list(Phi=list(formula=~sex+weight)))
mod2=mark(dipper,groups="sex",
  model.parameters=list(Phi=list(formula=~sex)))
mod3=mark(dipper,groups="sex",
  model.parameters=list(Phi=list(formula=~weight)))
mod4=mark(dipper,groups="sex",
  model.parameters=list(Phi=list(formula=~1)))
dipper.list=collect.models()
return(dipper.list)
}
dipper.results=run.dipper()
real.averages=model.average(dipper.results,vcv=TRUE)
# get model averaged estimates for all parameters and use average
# covariate values in models with covariates
real.averages$estimates
# get model averaged estimates for Phi using a value of 2 for weight
model.average(dipper.results,"Phi",
  data=data.frame(weight=2),vcv=FALSE)
# what you can't do yet is use different covariate values for
# different groups to get covariances of estimates based on different
# covariate values; for example, you can get average survival of females
# at average female weight and average survival of males at average
# male weight in separate calls to model.average but not in the same call
# to get covariances; however, if you standardized weight by group
# (ie stdwt = weight - groupmean) then using 0 for the covariate value would give
# the model averaged Phi by group at the average group weights and its
# covariance. You can do the above for
# a single model with find.covariates/fill.covariates.
# get model averaged estimates of first Phi(1) and first p(43) and v-c matrix
model.average(dipper.results,vcv=TRUE,indices=c(1,43))

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