odTest function

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))

Arguments

• glmobj: an object of class negbin produced by glm.nb
• alpha: significance level of over-dispersion test
• digits: number of digits in printed output

Details

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).

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.

Returns

None; prints results and returns silently

References

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.

Author(s)

Simon Jackman simon.jackman@sydney.edu.au . John Fox noted an error in an earlier version.

See Also

glm.nb, logLik

Examples

data(bioChemists)
modelnb <- MASS::glm.nb(art ~ .,
                 data=bioChemists,
                 trace=TRUE)
odTest(modelnb)