AICcmodavg (version 1.01)

modavg: Model-average Parameter Estimate (Multimodel Inference)

Description

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

Usage

modavg(cand.set, parm, modnames, c.hat = 1, gamdisp = NULL,
conf.level = 0.95, second.ord =
TRUE, nobs = NULL)
modavg.glm(cand.set, parm, modnames, c.hat = 1, gamdisp = NULL,
conf.level = 0.95, second.ord = TRUE, nobs = NULL) 
modavg.lme(cand.set, parm, modnames, conf.level = 0.95, second.ord =
TRUE, nobs = NULL)

Arguments

cand.set

a list storing each of the models in the candidate model set.

parm

the parameter of interest for which a model-averaged estimate is required.

modnames

a character vector of model names to facilitate the identification of each model in the model selection table.

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 either for binomial GLM's with trials > 1 (i.e., success/trial or cbind(success, failu

gamdisp

if gamma GLM is used, the dispersion parameter should be specified here to apply the same value to each model.

conf.level

the confidence level requested for the computation of unconditional confidence intervals.

second.ord

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

nobs

this argument allows to specify a numeric value other than total sample size to compute the AICc. This is relevant only for linear mixed models where sample size is not straightforward. In such cases, one might use total number of observations or number

Value

• 'modavg', 'modavg.glm', and 'modavg.lme' create an object of class 'modavg' with the following components:
• Parameter
  the parameter for which a model-averaged estimate was obtained
• Mod.avg.table
  the reduced model selection table based on models including the parameter of interest
• Mod.avg.beta
  the model-averaged estimate based on all models including the parameter of interest (see details above regarding the exclusion of models where parameter of interest is involved in an interaction)
• Uncond.SE
  the unconditional standard error for the model-averaged estimate (as opposed to the conditional SE based on a single model)
• Conf.level
  the confidence level used to compute the confidence interval
• Lower.CL
  the lower confidence limit
• Upper.CL
  the upper confidence limit

Details

The parameter must be specified as it appears in the model output. For factors, one must specify the name of the variable and the level of interest.

In cases where one desires a model-averaged estimate for a main effect term that is also involved in an interaction in certain models, modavg (correctly) excludes models with interactions involving the main effect term when it finds that the variable also appears in an interaction. Care must be taken when some models include interaction or polynomial terms, because main effect terms do not have the same interpretation when an interaction term appears in the same model. To avoid problems, one should use the usual operators to build interaction terms or polynomial terms. If polynomial or interaction terms are built manually, you should include the entire name of the variables involved because modavg( ) uses regexpr( ) to search for duplicates in model formula.

'modavg' is a function that calls either 'modavg.glm' or 'modavg.lme', depending on the class of the object. The current function is implemented for a list containing objects of 'lm','glm', and 'lme' classes.

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.

Burnham, K. P., Anderson, D. R. (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33, 261--304.

Mazerolle, M. J. (2006) Improving data analysis in herpetology: using Akaike's Information Criterion (AIC) to assess the strength of biological hypotheses. Amphibia-Reptilia 27, 169--180.

See Also

AICc, aictab, c_hat, importance, confset, evidence, modavgpred

Examples

#anuran larvae example from Mazerolle (2006)
data(min.trap)
#assign "UPLAND" as the reference level as in Mazerolle (2006)          
min.trap$Type <- relevel(min.trap$Type, ref = "UPLAND") 

#set up candidate models          
Cand.mod <- list()
#global model          
Cand.mod[[1]] <- glm(Num_anura ~ Type + log.Perimeter + Num_ranatra,
family = poisson, offset = log(Effort), data = min.trap) 
Cand.mod[[2]] <- glm(Num_anura ~ Type + log.Perimeter, family = poisson,
offset = log(Effort), data = min.trap) 
Cand.mod[[3]] <- glm(Num_anura ~ Type + Num_ranatra, family = poisson,
offset = log(Effort), data = min.trap) 
Cand.mod[[4]] <- glm(Num_anura ~ Type, family = poisson,
offset = log(Effort), data = min.trap) 
Cand.mod[[5]] <- glm(Num_anura ~ log.Perimeter + Num_ranatra,
family = poisson, offset = log(Effort), data = min.trap) 
Cand.mod[[6]] <- glm(Num_anura ~ log.Perimeter, family = poisson,
offset = log(Effort), data = min.trap) 
Cand.mod[[7]] <- glm(Num_anura ~ Num_ranatra, family = poisson,
offset = log(Effort), data = min.trap) 
Cand.mod[[8]] <- glm(Num_anura ~ 1, family = poisson,
offset = log(Effort), data = min.trap) 
          
#check c-hat for global model
c_hat(Cand.mod[[1]]) #uses Pearson's chi-square/df
#note the very low overdispersion: in this case, the analysis could be
#conducted without correcting for c-hat as its value is reasonably close
#to 1  

#assign names to each model
Modnames <- c("type + logperim + invertpred", "type + logperim", "type +
invertpred", "type", "logperim + invertpred", "logperim", "invertpred",
"intercept only") 

#compute model-averaged estimate of TypeBOG
modavg(parm = "TypeBOG", cand.set = Cand.mod, modnames = Modnames)


#compute residual deviance as in Mazerolle (2006)          
Cand.mod[[1]]$deviance/Cand.mod[[1]]$df.residual

#compute model-averaged estimate of TypeBOG as in Table 4 of
#Mazerolle (2006) 
modavg(parm = "TypeBOG", cand.set = Cand.mod, modnames = Modnames,
c.hat = 1.11)