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

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

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.

Details

useBICCustom computes one of the following two information criteria:

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

Value

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

Note

The actual (Q)BIC values are not really interesting in themselves, as they depend directly on the data, parameters estimated, and likelihood function. Furthermore, a single value does not tell much about model fit. Information criteria become relevant when compared to one another for a given data set and set of candidate models.

Author(s)

Marc J. Mazerolle

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

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##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)

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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