AICcmodavg (version 2.0-3)

modavgCustom: Compute Model-averaged Parameter Estimate (Multimodel Inference) from User-supplied Input

Description

This function model-averages the estimate of a parameter of interest among a set of candidate models, and computes the unconditional standard error and unconditional confidence intervals as described in Buckland et al. (1997) and Burnham and Anderson (2002).

Usage

modavgCustom(logL, K, modnames = NULL, estimate, se, second.ord = TRUE,
             nobs = NULL, uncond.se = "revised", conf.level = 0.95,
             c.hat = 1)

Arguments

logL

a vector of log-likelihood values for the models in the candidate model set.

K

a vector containing the number of estimated parameters for each model in the candidate model set.

modnames

a character vector of model names to facilitate the identification of each model in the model selection table. If NULL, the function uses the names in the cand.set list of candidate models. If no names appear in the list, generic names (e.g.

estimate

a vector of estimates for each of the models in the candidate model set. Estimates can be either beta estimates for a parameter of interest or a single prediction from each model.

se

a vector of standard errors for each of the estimates appearing in the estimate vector.

second.ord

logical. If TRUE, the function returns the second-order Akaike information criterion (i.e., AICc).

nobs

the sample size required to compute the AICc or QAICc.

uncond.se

either, "old", or "revised", specifying the equation used to compute the unconditional standard error of a model-averaged estimate. With uncond.se = "old", computations are based on equation 4.9 of Burnham and

conf.level

the confidence level ($1 - \alpha$) requested for the computation of unconditional confidence intervals.

c.hat

value of overdispersion parameter (i.e., variance inflation factor) such as that obtained from c_hat. Note that values of c.hat different from 1 are only appropriate for binomial GLM's with trials > 1 (i.e., success/trial or cbi

Value

• modavgCustom creates an object of class modavgCustom with the following components:
• Mod.avg.table
  the model selection table
• Mod.avg.est
  the model-averaged estimate
• Uncond.SE
  the unconditional standard error for the model-averaged estimate
• Conf.level
  the confidence level used to compute the confidence interval
• Lower.CL
  the lower confidence limit
• Upper.CL
  the upper confidence limit

Details

modavgCustom computes a model-averaged estimate from the vector of parameter estimates specified in estimate. Estimates and their associated standard errors must be specified in the same order as the log-likelihood, number of estimated parameters, and model names. Estimates provided may be for a parameter of interest (i.e., beta estimates) or predictions from each model. This function is most useful when model input is imported into R from other software (e.g., Program MARK, PRESENCE) or for model classes that are not yet supported by the other model averaging functions such as modavg or modavgPred.

References

Anderson, D. R. (2008) Model-based Inference in the Life Sciences: a primer on evidence. Springer: New York.

Buckland, S. T., Burnham, K. P., Augustin, N. H. (1997) Model selection: an integral part of inference. Biometrics 53, 603--618.

Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.

Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577--587.

Lebreton, J.-D., Burnham, K. P., Clobert, J., Anderson, D. R. (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case-studies. Ecological Monographs 62, 67--118.

MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A., Langtimm, C. A. (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83, 2248--2255.

Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108--115.

See Also

AICcCustom, aictabCustom modavg, modavgShrink, modavgPred

Examples

##model averaging parameter estimate (natural average)
##vector with model LL's
LL <- c(-38.8876, -35.1783, -64.8970)

##vector with number of parameters
Ks <- c(7, 9, 4)

##create a vector of names to trace back models in set
Modnames <- c("Cm1", "Cm2", "Cm3")

##vector of beta estimates for a parameter of interest
model.ests <- c(0.0478, 0.0480, 0.0478)

##vector of SE's of beta estimates for a parameter of interest
model.se.ests <- c(0.0028, 0.0028, 0.0034)

##compute model-averaged estimate and unconditional SE
modavgCustom(logL = LL, K = Ks, modnames = Modnames, 
             estimate = mode.ests, se = model.se.ests, nobs = 121)



##model-averaging with shrinkage
##set up candidate models
data(min.trap)
Cand.mod <- list( )
##global model          
Cand.mod[[1]] <- glm(Num_anura ~ Type + log.Perimeter,
                     family = poisson, offset = log(Effort),
                     data = min.trap) 
Cand.mod[[2]] <- glm(Num_anura ~ Type + Num_ranatra, family = poisson,
                     offset = log(Effort), data = min.trap) 
Cand.mod[[3]] <- glm(Num_anura ~ log.Perimeter + Num_ranatra,
                     family = poisson, offset = log(Effort), data = min.trap)
Model.names <- c("Type + log.Perimeter", "Type + Num_ranatra",
                 "log.Perimeter + Num_ranatra")
##model-averaged estimate with shrinkage (glm model type is already supported)
modavgShrink(cand.set = Cand.mod, modnames = Model.names,
             parm = "log.Perimeter")

##equivalent manual version of model-averaging with shrinkage
##this is especially useful when model classes are not supported
##extract vector of LL
LLs <- sapply(Cand.mod, FUN = function(i) logLik(i)[1])
##extract vector of K
Ks <- sapply(Cand.mod, FUN = function(i) attr(logLik(i), "df"))
##extract betas
betas <- sapply(Cand.mod, FUN = function(i) coef(i)["log.Perimeter"])
##second model does not include log.Perimeter
betas[2] <- 0
##extract SE's
ses <- sapply(Cand.mod, FUN = function(i) sqrt(diag(vcov(i))["log.Perimeter"]))
ses[2] <- 0
##extract
modavgCustom(logL = LLs, K = Ks, modnames = Model.names,
             nobs = nrow(min.trap), estimate = betas, se = ses)