AICcmodavg (version 2.3-1)

useBICCustom: Custom Computation of BIC and QBIC from User-supplied Input

Description

This function computes the Bayesian information criterion (BIC) or a quasi-likelihood counterpart (QBIC) from user-supplied input instead of extracting the values automatically from a model object. This function is particularly useful for output imported from other software or for model classes that are not currently supported by useBIC.

Usage

useBICCustom(logL, K, return.K = FALSE, nobs = NULL, c.hat = 1)

Value

useBICCustom returns the BIC or QBIC depending on the values of the c.hat argument.

Arguments

logL

the value of the model log-likelihood.

K

the number of estimated parameters in the model.

return.K

logical. If FALSE, the function returns the information criterion specified. If TRUE, the function returns K (number of estimated parameters) for a given model.

nobs

the sample size required to compute the BIC or QBIC.

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, useBICCustom will return the quasi-likelihood analogue of the information criterion requested.

Author

Marc J. Mazerolle

Details

useBICCustom computes one of the following two information criteria:

the Bayesian information criterion (BIC, Schwarz 1978) or the quasi-likelihood BIC (QBIC).

References

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.

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

AICc, aictabCustom, useBIC, bictab, evidence, modavgCustom

Examples

##cement data from Burnham and Anderson (2002, p. 101)
data(cement)
##run multiple regression - the global model in Table 3.2
glob.mod <- lm(y ~ x1 + x2 + x3 + x4, data = cement)

##extract log-likelihood
LL <- logLik(glob.mod)[1]

##extract number of parameters
##including residual variance
K.mod <- length(coef(glob.mod)) + 1

##compute BIC with full likelihood
useBICCustom(LL, K.mod, nobs = nrow(cement))
##compare against useBIC
useBIC(glob.mod)