Tests for Overdispertion | R Documentation |

When working with count data, the assumption of a Poisson model is common. However, sometimes the variance of the data is significantly higher that their mean which means that the assumption of that data have been drawn from a Poisson distribution is wrong.

In that case is is usually said that data are overdispersed and a better
model must be proposed. A good choice is a Negative Binomial distribution
(see, for example, `negative.binomial`

.

Tests for overdispersion available in this package are the Likelihood Ratio
Test (LRT) and Dean's `P_B`

and `P'_B`

tests.

```
test.nb.pois(x.nb, x.glm)
DeanB(x.glm, alternative="greater")
DeanB2(x.glm, alternative="greater")
```

`x.nb` |
Fitted Negative Binomial. |

`x.glm` |
Fitted Poisson model. |

`alternative` |
Alternative hipothesis to be tested. It can be "less", "greater" or "two.sided", although the usual choice will often be "greater". |

The LRT is computed to compare a fitted Poisson model against a fitted Negative Binomial model.

Dean's `P_B`

and `P'_B`

tests are score tests. These
two tests were proposed for the case in which we look for overdispersion
of the form
`var(Y_i)=\mu_i(1+\tau \mu_i)`

, where
`E(Y_i)=\mu_i`

.
See Dean (1992) for more details.

An object of type *htest* with the results (p-value, etc.).

Dean, C.B. (1992), Testing for overdispersion in Poisson and binomial regression models, *J. Amer. Statist. Assoc.* 87, 451-457.

DCluster, achisq.stat, pottwhit.stat, negative.binomial (MASS), glm.nb (MASS)

```
library(spdep)
library(MASS)
data(nc.sids)
sids<-data.frame(Observed=nc.sids$SID74)
sids<-cbind(sids, Expected=nc.sids$BIR74*sum(nc.sids$SID74)/sum(nc.sids$BIR74))
sids<-cbind(sids, x=nc.sids$x, y=nc.sids$y)
x.glm<-glm(Observed~1+offset(log(sids$Expected)), data=sids, family=poisson())
x.nb<-glm.nb(Observed~1+offset(log(Expected)), data=sids)
print(test.nb.pois(x.nb, x.glm))
print(DeanB(x.glm))
print(DeanB2(x.glm))
```

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