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

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4.6. Overdispersion

When estimating logit models with grouped data, it often happens that the model doesn’t fit—the deviance and Pearson chi-square are large, relative to the degrees of freedom. Lack of fit is sometimes described as overdispersion. Overdispersion has two possible causes:

  • An incorrectly specified model: more interactions and/or nonlinearities are needed in the model.

  • Lack of independence of the observations: this can arise from unobserved heterogeneity that operates at the level of groups rather than individuals.

We’ve already seen examples of the first cause. Now let’s look at an example where overdispersion may arise from dependence among the observations. The sample consists of 40 U.S. biochemistry departments in the late 1950s ...

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