odTest | R Documentation |

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^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.

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.

`glm.nb`

, `logLik`

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

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.