R: Compute model averaged estimates of real parameters from a...

model.average.list

R Documentation

Compute model averaged estimates of real parameters from a list structure for estimates

Description

A generic function to compute model averaged estimates and their standard errors or variance-covariance matrix

Usage

## S3 method for class 'list'
model.average(x, revised=TRUE, mata=FALSE, normal.lm=FALSE, 
                                       residual.dfs=0, alpha=0.025,...)

Arguments

`x`	a list containing the following elements: 1) `estimate` - a vector or matrix of estimates, 2)a vector of model selection criterion value named `AIC,AICc,QAIC,QAICc` or a `weight` variable that sums to 1 across models, and 3) a vector or matrix named `se` which give the model-specific standard errors for each estimate or a list of matrices named `vcv` which give the model-specific variance-covariance matrices.
`revised`	if TRUE it uses eq 6.12 from Burnham and Anderson (2002) for model averaged se; otherwise it uses eq 4.9
`mata`	if TRUE, create model averaged tail area confidence intervals as described by Turek and Fletcher
`normal.lm`	Specify normal.lm=TRUE for the normal linear model case, and normal.lm=FALSE otherwise. When normal.lm=TRUE, the argument 'residual.dfs' must also be supplied. See USAGE section, and Turek and Fletcher (2012) for additional details.
`residual.dfs`	A vector containing the residual (error) degrees of freedom under each candidate model. This argument must be provided when the argument normal.lm=TRUE.
`alpha`	The desired lower and upper error rate. Specifying alpha=0.025 corresponds to a 95 alpha=0.05 to a 90 Default value is alpha=0.025.
`...`	additional arguments passed to specific functions

Details

If a single estimate is being model-averaged then estimate and se are vectors with an entry for each model. However, if there are several estimates being averaged then both estimate and se should be matrices in which the estimates for each model are a row in the matrix. Regardless, if vcv is specified it should be a list of matrices and in the case of a single estimate, each matrix is 1x1 containing the estimated sample-variance but that would be rather useless and se should be used instead.

If the list contains an element named AIC,AICc,QAIC, or QAICc, then the minimum value is computed and subtracted to compute delta values relative to the minimum. These are then converted to Akaike weights which are exp(-.5*delta) and these are normalized to sum to 1. If the list does not contain one of the above values then it should have a variable named weight. It is normalized to 1. The model-averaged estimates are computed using equation 4.1 of Burnham and Anderson (2002).

If the contains a matrix named vcv, then a model-averaged variance-covariance matrix is computed using formulae given on page 163 of Burnham and Anderson (2002). If there is no element named vcv then there must be an element se which contains the model-specific estimates of the standard errors. The unconditional standard error for the model-averaged estimates is computed using equation 4.9 of Burnham and Anderson (2002) if if revised=FALSE; otherwise it uses eq 6.12.

Value

A list containing elements:

`estimate`	vector of model-averaged estimates
`se`	vector of unconditional standard errors (square root of unconditional variance estimator)
`vcv`	model-averaged variance-covariance matrix if `vcv` was specified input list
`lcl`	lower confidence interval if mata=TRUE
`ucl`	upper confidence interval if mata=TRUE

Author(s)

Jeff Laake

References

BURNHAM, K. P., AND D. R. ANDERSON. 2002. Model selection and multimodel inference. A practical information-theoretic approach. Springer, New York. Turek, D. and Fletcher, D. (2012). Model-Averaged Wald Confidence Intervals. Computational Statistics and Data Analysis, 56(9), p.2809-2815.

Examples


# This example is excluded from testing to reduce package check time
# Create a set of models from dipper data
data(dipper)
run.dipper=function()
{
dipper$nsex=as.numeric(dipper$sex)-1
mod1=mark(dipper,groups="sex",
   model.parameters=list(Phi=list(formula=~sex)),delete=TRUE)
mod2=mark(dipper,groups="sex",
   model.parameters=list(Phi=list(formula=~1)),delete=TRUE)
mod3=mark(dipper,groups="sex",
   model.parameters=list(p=list(formula=~time),
   Phi=list(formula=~1)),delete=TRUE)
dipper.list=collect.models()
return(dipper.list)
}
dipper.results=run.dipper()
# Extract indices for first year survival from 
#  Females (group 1) and Males (group 2)
Phi.indices=extract.indices(dipper.results[[1]],
   "Phi",df=data.frame(group=c(1,2),row=c(1,1),col=c(1,1)))
# Create a matrix for estimates
estimate=matrix(0,ncol=length(Phi.indices),
    nrow=nrow(dipper.results$model.table))
# Extract weights for models
weight=dipper.results$model.table$weight
# Create an empty list for vcv matrices
vcv=vector("list",length=nrow(dipper.results$model.table))
# Loop over each model in model.table for dipper.results
for (i in 1:nrow(dipper.results$model.table))
{
# The actual model number is the row number for the model.table
  model.numbers= as.numeric(row.names(dipper.results$model.table))
# For each model extract those real parameter values and their
# vcv matrix and store them
  x=covariate.predictions(dipper.results[[model.numbers[i]]],
      data=data.frame(index=Phi.indices))
  estimate[i,]=x$estimates$estimate
  vcv[[i]]=x$vcv
}
# Call model.average using the list structure which includes 
#  estimate, weight and vcv list in this case
model.average(list(estimate=estimate,weight=weight,vcv=vcv))
#
# Now get same model averaged estimates using model.average.marklist
# Obviously this is a much easier approach and what would be used 
# if all you are doing is model averaging real parameters in the model.  
# The other form is more useful for model averaging
# functions of estimates of the real parameters (eg population estimate)
#
mavg=model.average(dipper.results,"Phi",vcv=TRUE)
print(mavg$estimates[Phi.indices,])
print(mavg$vcv.real[Phi.indices,Phi.indices])