Equality of variance in Poisson regression

[ammarhm]

Hi everyone, 

I am really struggling with the analysis of equality of variance as one of the assumptions of Poisson regression. 

Here is what I am doing:

proc glimmix data=have;
by group;
class disease sex;
effect yearspline=spline(year / naturalcubic knotmethod=equal(5));
effect agespline=spline(age / naturalcubic knotmethod=equal(5));
model events=disease sex aspl yspl / dist=poisson offset=logtime s cl link=log;
random _residual_/group=disease;
covtest homogeneity;
run;

I am doing the right thing with covtest? 

The result of 'test of covariance parameters based on residual pseudo likelihhod' is coming with a Homogeneity p value of <0.0001. Does that mean that there is significant difference in the variance between the 'disease' groups and that the quality of variance assumption for poisson regression is not met, and hence I should not be using this Poisson model? 

Thanks 

[StatDave]

Equal variances are only assumed for models on normally distributed responses. Poisson regression and most other generalized linear models do not make this assumption. See this note. 

[ammarhm]

Thank you @StatDave  you are absolutely correct, my bad, i should have siad 'equality of variance and mean'.

So what i am actually trying to do is to test the assumption that  the mean and variance are equal in my data/model...

Any suggestions/thoughts on how to do that and if my code up is right?

Thank you

[StatDave · Accepted solution]

Yes, the Poisson assumes equal mean and variance. It is not uncommon for the variance to exceed the mean and this is known as overdispersion. Underdispersion (variance less than the mean) can also happen but is less common. The negative binomial distribution has an extra component that can accommodate the inequality, so it is often used with overdispersed data. But you can also use it as a test for overdispersion by testing that the extra variance component is zero. You do this by specifying the DIST=NEGBIN SCALE=0 NOSCALE options in the MODEL statement in PROC GENMOD. Overdispersion is indicated if the additional test that it presents is significant. This note discusses overdispersion and various strategies for this situation.