# odTest

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

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

- Keywords
- regression

##### 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 \(\chi^2_1\) 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.

##### Value

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.

##### See Also

##### Examples

```
# NOT RUN {
data(bioChemists)
modelnb <- MASS::glm.nb(art ~ .,
data=bioChemists,
trace=TRUE)
odTest(modelnb)
# }
```

*Documentation reproduced from package pscl, version 1.4.9, License: GPL-2*