R: likelihood ratio test for over-dispersion in count data

odTest {pscl} | R Documentation

## likelihood ratio test for over-dispersion in count data

### Description

Compares the log-likelihoods of a negative binomial regression model and a Poisson regression model.

### Usage

    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.

### Value

None; prints results and returns silently

### Author(s)

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

### 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.

### See Also

`glm.nb`, `logLik`

### Examples

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

[Package pscl version 1.5.2 Index]