Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 |

`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-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.

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.

1 2 3 4 5 | ```
data(bioChemists)
modelnb <- MASS::glm.nb(art ~ .,
data=bioChemists,
trace=TRUE)
odTest(modelnb)
``` |

```
Loading required package: MASS
Loading required package: lattice
Classes and Methods for R developed in the
Political Science Computational Laboratory
Department of Political Science
Stanford University
Simon Jackman
hurdle and zeroinfl functions by Achim Zeileis
Theta(1) = 2.268830, 2(Ls - Lm) = 1004.930000
Theta(2) = 2.264410, 2(Ls - Lm) = 1004.280000
Theta(3) = 2.264400, 2(Ls - Lm) = 1004.280000
Theta(4) = 2.264390, 2(Ls - Lm) = 1004.280000
Theta(5) = 2.264390, 2(Ls - Lm) = 1004.280000
Theta(6) = 2.264390, 2(Ls - Lm) = 1004.280000
Theta(7) = 2.264390, 2(Ls - Lm) = 1004.280000
Theta(8) = 2.264390, 2(Ls - Lm) = 1004.280000
Likelihood ratio test of H0: Poisson, as restricted NB model:
n.b., the distribution of the test-statistic under H0 is non-standard
e.g., see help(odTest) for details/references
Critical value of test statistic at the alpha= 0.05 level: 2.7055
Chi-Square Test Statistic = 180.196 p-value = < 2.2e-16
```

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