modavgIC function

Compute Model-averaged Parameter Estimate from User-supplied Information Criterion

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). Computations are based on the values of the information criterion supplied manually by the user. 1.1

modavgIC(ic, K, modnames = NULL, estimate, se, uncond.se = "revised",
         conf.level = 0.95, 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.
• 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.
• 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 Anderson (2002), which was the former way to compute unconditional standard errors. With uncond.se = "revised", equation 6.12 of Burnham and Anderson (2002) is used. Anderson (2008, p. 111) recommends use of the revised version for the computation of unconditional standard errors and it is now the default.
• conf.level: the confidence level ($1 - \alpha$) requested for the computation of unconditional confidence intervals.
• 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

modavgIC 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 values of the information criterion, the number of estimated parameters, and the 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 for information criterion other than AIC, AICc, QAIC, and QAICc (e.g., WAIC: Watanabe 2010) or for classes not supported by modavg, modavgCustom, or modavgPred.

Returns

modavgIC creates an object of class modavgIC 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.

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.

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, ictab, modavg, modavgCustom, modavgShrink, modavgPred

Examples

## Not run:

##model averaging parameter estimate based on WAIC
##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)

##vector of predictions
Preds <- c(0.106, 0.137, 0.067, 0.050)
##vector of SE's for prediction
Ses <- c(0.128, 0.159, 0.054, 0.039)

##compute model-averaged estimate and unconditional SE based on WAIC
modavgIC(ic = waic, K = effK, modnames = Modnames, 
         estimate = Preds, se = Ses,
         ic.name = "WAIC")
## End(Not run)