How do you choose between Poisson and negative binomial models for discrete count outcomes?
One key criterion is the relative value of the variance to the mean after accounting for the effect of the predictors. A previous article discussed the concept of a variance that is larger than the model assumes: overdispersion.
(Underdispersion is also possible, but much less common).
There are two ways to check for overdispersion: (more…)
If you have count data you use a Poisson model for the analysis, right?
The key criterion for using a Poisson model is after accounting for the effect of predictors, the mean must equal the variance. If the mean doesn’t equal the variance then all we have to do is transform the data or tweak the model, correct?
Let’s see how we can do this with some real data. A survey was done in Australia during the peak of the flu season. The outcome variable is the total number of times people asked for medical advice from any source over a two-week period.
We are trying to determine what influences people with flu symptoms to seek medical advice. The mean number of times was 0.516 times and the variance 1.79.
The mean does not equal the variance even after accounting for the model’s predictors.
Here are the results for this model: (more…)
In my last blog post we fitted a generalized linear model to count data using a Poisson error structure.
We found, however, that there was over-dispersion in the data – the variance was larger than the mean in our dependent variable.