Longitudinal studies of a binary outcome are common in the health, social,
and behavioral sciences. In general, a feature of random effects logistic
regression models for longitudinal binary data is that the marginal functional
form, when integrated over the distribution of the random effects, is no longer
of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775]
proposed a random intercept model in the clustered binary data setting where
the marginal model has a logistic form.