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
the value of the model log-likelihood.
the number of estimated parameters in the model.
the sample size required to compute the BIC or QBIC.
value of overdispersion parameter (i.e., variance inflation factor)
such as that obtained from
useBICCustom computes one of the following two information
the Bayesian information criterion (BIC, Schwarz 1978) or the quasi-likelihood BIC (QBIC).
useBICCustom returns the BIC or QBIC depending on the values of
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.
Marc J. Mazerolle
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.
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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) ##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)