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A friend and I are having a dis-agreement about over-dispersion in binomial/logistic regression glm modelling. We have structured our data so that each observation represents 1 Bernoulli trial (so the response is strictly either 0 or 1) and are using logistic regression to build a model.

Is it possible for there to be over-dispersion in this model (or is the scale parameter necessarily 1)? If so, why? And if we need one, what is the best scale parameter estimator to use (we'll have a very low response - sub 1%).

Thanks, Tom

TomFromWales
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1 Answers1

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If the observations are independent it is impossible to have overdispersion with Bernoulli responses. I'm not sure what made the question arise. If the regression model is improperly specified you will have a different problem. For example in a logistic model, a strong omitted covariate can cause all the $\beta$s to be biased towards zero due to non-collapsibility of the odds ratio.

Frank Harrell
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