Compares the log-likelihoods of a negative binomial regression model and a Poisson regression model.
odTest(glmobj, alpha=.05, digits = max(3, getOption("digits") - 3))None; prints results and returns silently
an object of class negbin produced by
glm.nb
significance level of over-dispersion test
number of digits in printed output
Simon Jackman simon.jackman@sydney.edu.au. John Fox noted an error in an earlier version.
The negative binomial model relaxes the assumption in the
Poisson model that the (conditional) variance equals the (conditional)
mean, by estimating one extra parameter. A likelihood ratio (LR) test
can be used to test the null hypothesis that the restriction implicit
in the Poisson model is true. The LR test-statistic has a non-standard
distribution, even asymptotically, since the negative binomial
over-dispersion parameter (called theta in glm.nb) is
restricted to be positive. The asymptotic distribution of the LR
(likelihood ratio) test-statistic has probability mass of one half at
zero, and a half \(\chi^2_1\) distribution above
zero. This means that if testing at the \(\alpha\) = .05
level, one should not reject the null unless the LR test statistic
exceeds the critical value associated with the \(2\alpha\)
= .10 level; this LR test involves just one parameter restriction, so
the critical value of the test statistic at the \(p\) = .05 level
is 2.7, instead of the usual 3.8 (i.e., the .90 quantile of the
\(\chi^2_1\) distribution, versus the .95 quantile).
A Poisson model is run using glm with family set to
link{poisson}, using the formula in the negbin
model object passed as input. The logLik functions are
used to extract the log-likelihood for each model.
A. Colin Cameron and Pravin K. Trivedi (1998) Regression analysis of count data. New York: Cambridge University Press.
Lawless, J. F. (1987) Negative Binomial and Mixed Poisson Regressions. The Canadian Journal of Statistics. 15:209-225.
data(bioChemists)
modelnb <- MASS::glm.nb(art ~ .,
data=bioChemists,
trace=TRUE)
odTest(modelnb)
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