This chapter can be considered as a continuation of the previous one. Few real-life Poisson data sets are truly equidispersed. Overdispersion to some degree is inherent to the vast majority of Poisson data. Thus, the real question deals with the amount of overdispersion in a particular model – is it statistically sufficient to require a model other than Poisson? This is a foremost question we address in this chapter, together with how we differentiate between real and apparent overdispersion.

What is overdispersion?

Not all overdispersion is real; apparent overdispersion may sometimes be identified and the model amended to eliminate it. We first address the difference between real and apparent overdispersion, and what can be done about the latter.

1. 1 What is overdispersion?

2. Overdispersion in Poisson models occurs when the response variance is greater than the mean.

3. 2 What causes overdispersion?

4. Overdispersion is caused by positive correlation between responses or by an excess variation between response probabilities or counts. Overdispersion also arises when there are violations in the distributional assumptions of the data, such as when the data are clustered and thereby violate the likelihood independence of observations assumption.

5. 3 Why is overdispersion a problem?

6. Overdispersion may cause standard errors of the estimates to be deflated or underestimated, i.e. a variable may appear to be a significant predictor when it is in fact not significant.

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