Common Errors in Statistics (and How to Avoid Them), 4th Edition

SUBJECT-SPECIFIC OR POPULATION-AVERAGED?

A favorite example in comparing subject-specific and population-averaged estimators is to consider the difference in interpretation of regression coefficients for a binary outcome model on whether a child will exhibit symptoms of respiratory illness. The predictor of interest is whether or not the child’s mother smokes. Thus, we have repeated observations on children and their mothers. If we were to fit a subject-specific model, we would interpret the coefficient on smoking as the change in likelihood of respiratory illness as a result of the mother switching from not smoking to smoking.

On the other hand, the interpretation of the coefficient in a population-averaged model is the likelihood of respiratory illness for the average child with a nonsmoking mother compared to the likelihood for the average child with a smoking mother. Both models offer equally valid interpretations. The interpretation of interest should drive model selection; some studies ultimately will lead to fitting both types of models.

An approximate answer to the right question is worth a good deal more than the exact answer to an approximate problem.

—John W. Tukey