ictab function

Create Model Selection Tables from User-supplied Information Criterion

This function creates a model selection table from information criterion values supplied by the user. The table ranks the models based on the values of the information criterion and also displays delta values and information criterion weights. 1.1

ictab(ic, K, modnames = NULL, sort = TRUE, ic.name = NULL)

Arguments

• ic: a vector of information criterion values for each model 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 identify each model in the model selection table. If NULL, generic names (e.g., Mod1, Mod2) are supplied in the table in the same order as the information criterion values.
• sort: logical. If TRUE, the model selection table is ranked according to the values of the information criterion.
• ic.name: a character string denoting the name of the information criterion input by the user. This character string will appear in certain column labels of the model selection table.

Details

ictab constructs a model selection table based on the information criterion values supplied by the user. This function is most useful for information criterion other than AIC, AICc, QAIC, and QAICc (e.g., WAIC: Watanabe 2010) or for classes not supported by aictab or bictab.

Returns

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

• Modname: the name of each model of the candidate model set.

• K: the number of estimated parameters for each model.

• IC: the values of the information criterion input by the user. If a value for ic.name is provided, the table modifies the labels of the table.

• Delta_IC: the delta information criterion component comparing each model to 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.

• ICWt: the information criterion weights, also termed "model probabilities" 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 information criterion weights. These are only meaningful if results in table are sorted in decreasing order of Akaike weights (i.e., sort = TRUE).

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.

Watanabe, S. (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research 11 , 3571--3594.

Author(s)

Marc J. Mazerolle

See Also

aictabCustom, confset, evidence, modavgCustom, modavgIC

Examples

##create a vector of names to trace back models in set
Modnames <- c("global model", "interactive model",
              "additive model", "invertpred model")

##WAIC values
waic <- c(105.74, 107.36, 108.24, 100.57)
##number of effective parameters
effK <- c(7.45, 5.61, 6.14, 6.05)

##generate WAIC table
ictab(ic = waic, K = effK, modnames = Modnames,
      sort = TRUE, ic.name = "WAIC")