Abstract

Distinguishing between longitudinal dependence due to the effects of previous responses on subsequent responses and dependence due to unobserved heterogeneity is important in many disciplinesFor example, wheezing is an inflammatory reaction that may 'remodel' a child's airway structure and thereby affect the probability of future wheezing Alternatively, children could vary in their susceptibilities because of unobserved covariates such as genes For binary responses, distinguishing between state dependence and unobserved heterogeneity is typically accomplished by using dynamic/transition models that include both a lagged response and a random interceptNaive maximum likelihood estimators can be severely inconsistent because of two kinds of endogeneity problem: lack of independence of the initial response and the random intercept and lack of independence of the covariates and the random intercept We clarify and unify previous work on handling these problems in the disconnected literatures of statistics and econometrics, suggest improved methods, investigate the asymptotic performance of competing methods and provide practical recommendationsThe recommended methods are applied to longitudinal data on children's wheezing, where we investigate the extent of state dependence and unobserved heterogeneity and whether there is an effect of maternal smoking© 2013 Royal Statistical Society.