odTest {pscl} | R Documentation |
Compares the log-likelihoods of a negative binomial regression model and a Poisson regression model
odTest(glmobj, digits = max(3, getOption("digits") - 3))
glmobj |
an object of class negbin produced by glm.nb |
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 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 p = .05 level, we should not reject the null unless the LR test-statistic exceeds the critical value associated with the p = .025 level; this LR test involves just one parameter restriction, so the critical value of the test statistic at the p = .05 test statistic is 5.02, instead of the usual 3.8 (i.e., the .975 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.
None; prints results and returns silently
Simon Jackman <jackman@stanford.edu>
A. Colin Cameron and Pravin K. Trivedi (1998) Regression analysis of count data. New York: Cambridge University Press.
data(bioChemists) require(MASS) modelnb <- glm.nb(art ~ ., data=bioChemists, trace=TRUE) odTest(modelnb)