DCluster (version 0.2-7)

Tests for Overdispertion: Likelihood Ratio Test and Dean's Tests for Overdispertion

Description

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.

Usage

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

Arguments

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".

Value

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

Details

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.

References

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

See Also

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

Examples

# NOT RUN {
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))

# }