# Analysing overdispersed data with generalised linear models

Let's say I have an explanatory variable and a response variable that represents counts. I want to see if the explanatory variable can predicts counts. I'm aware the response variable is overdispersed. What I probably should do is analyse the data with a generalised linear model using the negative binomial distribution. But let's say I ignore the overdispersion and analyse the data using poisson regression.

What would be consequences of analysing these data with a poisson distribution? Would consequences be the same as ignoring heteroscedasticity in linear regression therefore incorrect standard errors/P-values?

• unless there are multiple observations that share exactly the same sets of predictions, overdispersion is unidentifiable in binary data. – Ben Bolker Mar 30 '14 at 17:57
• Question edited. I'm interested in whether the same issues that apply in linear regression also apply in generalised linear models – luciano Mar 30 '14 at 18:16
• Ben: regarding overdispersion in binary data, you might want to respond to this question: stats.stackexchange.com/questions/91597/… – luciano Mar 30 '14 at 18:21

One alternative is to fit a quasi-Poisson regression; it will scale the parameter variance estimates for the variation in the data (by using a variance of $\phi \mu$ with $\phi$ being able to be larger than 1).