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Logistic Regression Using SAS®: Theory and Application by Paul D. Allison

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9.4. Overdispersion

I now claim that the standard errors, chi-squares, and p-values in the previous section are essentially worthless because of overdispersion. We encountered overdispersion with grouped-data logit models in Chapter 4 where I argued that the problem was primarily restricted to clustered data. For Poisson regression, it’s always a potential problem, and often a quite serious one.

Basically the problem arises because equation (9.2) says that, for a given set of values on the explanatory variables, the variance of the dependent variable is equal to its mean. In fact, the variance is often much higher than that. Equivalently, we can say that overdispersion occurs because there’s no random disturbance term in equation (9.3) that ...

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