likelihood ratio test for over-dispersion in count data
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))glmobj |
an object of class |
alpha |
significance level of over-dispersion test |
digits |
number of digits in printed output |
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-square (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-square (1) distribution, versus the .95 quantile).
None; prints results and returns silently
Simon Jackman simon.jackman@sydney.edu.au. John Fox noted an error in an earlier version.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.