bictabCustom {AICcmodavg}

Create Model Selection Tables from User-supplied Input Based on (Q)BIC

Description

This function creates a model selection table from model input (log-likelihood, number of estimated parameters) supplied by the user instead of extracting the values automatically from a list of candidate models. The models are ranked based on the BIC (Schwarz 1978) or on a quasi-likelihood analogue (QBIC) corrected for overdispersion. The table ranks the models based on the selected information criteria and also provides delta BIC and BIC weights.

Usage

bictabCustom(logL, K, modnames = NULL, nobs = NULL, sort = TRUE,
             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 (i.e., a named list). If no names appear in the list and no character vector is provided, generic names (e.g., Mod1, Mod2) are supplied in the table in the same order as in the list of candidate models.

nobs

the sample size required to compute the AICc or QAICc.

sort

logical. If TRUE, the model selection table is ranked according to the (Q)BIC values.

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 cbind(success, failure) syntax), with Poisson GLM's, single-season or dynamic occupancy models (MacKenzie et al. 2002, 2003), N-mixture models (Royle 2004, Dail and Madsen 2011), or capture-mark-recapture models (e.g., Lebreton et al. 1992). If c.hat > 1, bictabCustom will return the quasi-likelihood analogue of the information criterion requested.

Details

bictabCustom constructs a model selection table based on BIC or QBIC. 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 bictab.

Value

bictabCustom creates an object of class bictab with the following components:

Modname

the name of each model of the candidate model set.

K

the number of estimated parameters for each model.

(Q)BIC

the information criteria requested for each model (BIC, QBIC).

Delta_(Q)BIC

the appropriate delta BIC component depending on the information criteria selected.

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.

(Q)BICWt

the BIC 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 BIC weights. These are only meaningful if results in table are sorted in decreasing order of BIC weights (i.e., sort = TRUE).

c.hat

if c.hat was specified as an argument, it is included in the table.

LL

if c.hat = 1 and parameters estimated by maximum likelihood, the log-likelihood of each model.

Quasi.LL

if c.hat > 1, the quasi log-likelihood of each model.

Author(s)

Marc J. Mazerolle

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.

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.

MacKenzie, D. I., Nichols, J. D., Hines, J. E., Knutson, M. G., Franklin, A. B. (2003) Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84, 2200–2207.

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.

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

Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461–464.

See Also

AICcCustom, aictabCustom, confset, c_hat, evidence, ictab, modavgCustom

Examples

##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")

##generate BIC table
bictabCustom(logL = LL, K = Ks, modnames = Modnames, nobs = 121,
             sort = TRUE)