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

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)=μ_i(1+τ μ_i), where E(Y_i)=μ_i. See Dean (1992) for more details.

Value

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

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

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))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(DCluster)
Loading required package: boot
Loading required package: spdep
Loading required package: sp
Loading required package: Matrix
Loading required package: MASS
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DCluster/dean_test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Tests for Overdispertion
> ### Title: Likelihood Ratio Test and Dean's Tests for Overdispertion
> ### Aliases: test.nb.pois DeanB DeanB2
> ### Keywords: htest
> 
> ### ** Examples
> 
> 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))

	Likelihood ratio test for overdispersion

data:  x.nb : x.glm
LR = 36.421, = 1, p-value = 1.589e-09
sample estimates:
       zscore  p.mayor.modZ 
-6.033594e+00  1.603523e-09 

> print(DeanB(x.glm))

	Dean's P_B test for overdispersion

data:  x.glm
P_B = 7.2275, p-value = 2.459e-13
alternative hypothesis: greater

> print(DeanB2(x.glm))

	Dean's P'_B test for overdispersion

data:  x.glm
P'_B = 7.3358, p-value = 1.102e-13
alternative hypothesis: greater

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>