dictab: Create Model Selection Tables from Bayesian Analyses

Description

This function creates a model selection table based on the deviance information criterion (DIC). The table ranks the models based on the DIC and also provides delta DIC and DIC weights. dictab selects the appropriate function to create the model selection table based on the object class. The current version works with objects of bugs, rjags, jagsUI classes.

Usage

dictab(cand.set, modnames = NULL, sort = TRUE, ...)
# S3 method for AICbugs
dictab(cand.set, modnames = NULL, sort = TRUE, ...)
# S3 method for AICrjags
dictab(cand.set, modnames = NULL, sort = TRUE, ...)
# S3 method for AICjagsUI
dictab(cand.set, modnames = NULL, sort = TRUE, ...)

Value

dictab creates an object of class dictab with the following components:

Modname: the name of each model of the candidate model set.
pD: the effective number of estimated parameters for each model.
DIC: the deviance information criterion for each model.
Delta_DIC: the delta DIC of each model, measuring the difference in DIC between each model and the top-ranked model.
ModelLik: the relative likelihood of the model given the data (exp(-0.5*delta[i])). This is not to be confused with the likelihood of the parameters given the data. The relative likelihood can then be normalized across all models to get the model probabilities.
DICWt: the DIC weights, sensu Burnham and Anderson (2002) and Anderson (2008). These measures indicate the level of support (i.e., weight of evidence) in favor of any given model being the most parsimonious among the candidate model set.
Cum.Wt: the cumulative DIC weights. These are only meaningful if results in table are sorted in decreasing order of DIC weights (i.e., sort = TRUE).
Deviance: the deviance of each model.

Arguments

cand.set: a list storing each of the models 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., Mod1, Mod2) are supplied in the table in the same order as in the list of candidate models.
sort: logical. If TRUE, the model selection table is ranked according to the DIC values.
...: additional arguments passed to the function.

Author

Marc J. Mazerolle

Details

dictab internally creates a new class for the cand.set list of candidate models, according to the contents of the list. The current function is implemented for bugs, jags, jagsUI classes. The function constructs a model selection table based on the DIC (Spiegelhalter et al. 2002). Note that DIC might not be appropriate to select among a set of hierarchical models and that modifications to the information criterion have been proposed (Millar 2009).

References

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

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

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., van der Linde, A. (2002). Bayesian measures of complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583--639.

Examples

Run this code

##from ?jags example in R2jags package
if (FALSE) {
require(R2jags)
model.file <- system.file(package="R2jags", "model", "schools.txt")
file.show(model.file)     

##data
J <- 8.0
y <- c(28.4,7.9,-2.8,6.8,-0.6,0.6,18.0,12.2)
sd <- c(14.9,10.2,16.3,11.0,9.4,11.4,10.4,17.6)
     
     
jags.data <- list (J = J, y = y, sd = sd)
jags.inits <- function(){
  list(theta=rnorm(J, 0, 100), mu=rnorm(1, 0, 100),
       sigma=runif(1, 0, 100))
}
jags.parameters <- c("theta", "mu", "sigma")
     
##run model
schools.sim <- jags(data = jags.data, inits = jags.inits,
                    parameters = jags.parameters,
                    model.file = model.file,
                    n.chains = 3, n.iter = 10)
#note that n.iter should be higher

##set up in list
Cand.mods <- list(schools.sim)
Model.names <- "hierarchical model"
##other models can be added to Cand.mods
##to compare them to the top model

##model selection table
dictab(cand.set = Cand.mods, modnames = Model.names)
detach(package:R2jags)
}

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