Functions to compute the Bayesian information criterion (BIC) or a quasi-likelihood analogue (QBIC).
useBIC(mod, return.K = FALSE, nobs = NULL, ...) # S3 method for aov
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for betareg
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for clm
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for clmm
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for coxme
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for coxph
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for fitdist
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for fitdistr
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for glm
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat = 1,
...)
# S3 method for glmmTMB
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat = 1,
...)
# S3 method for gls
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for gnls
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for hurdle
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for lavaan
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for lm
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for lme
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for lmekin
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for maxlikeFit
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat =
1, ...)
# S3 method for mer
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for merMod
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for lmerModLmerTest
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for multinom
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat = 1,
...)
# S3 method for nlme
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for nls
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for polr
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for rlm
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for survreg
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
# S3 method for unmarkedFit
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat =
1, ...)
# S3 method for vglm
useBIC(mod, return.K = FALSE, nobs = NULL, c.hat = 1,
...)
# S3 method for zeroinfl
useBIC(mod, return.K = FALSE, nobs = NULL, ...)
useBIC returns the BIC or the number of estimated parameters,
depending on the values of the arguments.
an object of class aov, betareg, clm,
clmm, clogit, coxme, coxph,
fitdist, fitdistr, glm, glmmTMB,
gls, gnls, hurdle, lavaan, lm,
lme, lmekin, maxlikeFit, mer,
merMod, lmerModLmerTest, multinom, nlme,
nls, polr, rlm, survreg, vglm,
zeroinfl, and various unmarkedFit classes containing
the output of a model.
logical. If FALSE, the function returns the information
criterion specified. If TRUE, the function returns K (number
of estimated parameters) for a given model.
this argument allows to specify a numeric value other than total
sample size to compute the BIC (i.e., nobs defaults to total
number of observations). This is relevant only for mixed models or
various models of unmarkedFit classes where sample size is not
straightforward. In such cases, one might use total number of
observations or number of independent clusters (e.g., sites) as the
value of nobs.
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 occupancy models (MacKenzie et al. 2002),
dynamic occupancy models (MacKenzie et al. 2003), or N-mixture
models (Royle 2004, Dail and Madsen 2011). If c.hat > 1,
useBIC will return the quasi-likelihood analogue of the
information criteria requested and multiply the variance-covariance
matrix of the estimates by this value (i.e., SE's are multiplied by
sqrt(c.hat)). This option is not supported for generalized
linear mixed models of the mer or merMod classes.
additional arguments passed to the function.
Marc J. Mazerolle
useBIC computes the Bayesian information criterion (BIC,
Schwarz 1978): $$BIC = -2 * log-likelihood + K * log(n),$$ where
the log-likelihood is the maximum log-likelihood of the model, K
corresponds to the number of estimated parameters, and n
corresponds to the sample size of the data set.
In the presence of overdispersion, a quasi-likelihood analogue of
the BIC (QBIC) will be computed, as $$QBIC = \frac{-2 *
log-likelihood}{c-hat} + K * log(n),$$ where c-hat is the
overdispersion parameter specified by the user with the argument
c.hat. Note that BIC or QBIC values are meaningful to select
among gls or lme models fit by maximum likelihood.
BIC or QBIC based on REML are valid to select among different models
that only differ in their random effects (Pinheiro and Bates 2000).
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.
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.
Pinheiro, J. C., Bates, D. M. (2000) Mixed-effect models in S and S-PLUS. Springer Verlag: New York.
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.
AICc, bictab,
bictabCustom, useBICCustom
##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)
##compute BIC with full likelihood
useBIC(glob.mod, return.K = FALSE)
##compute BIC for mixed model on Orthodont data set in Pinheiro and
##Bates (2000)
if (FALSE) {
require(nlme)
m1 <- lme(distance ~ age, random = ~1 | Subject, data = Orthodont,
method= "ML")
useBIC(m1, return.K = FALSE)
}
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