Maximum likelihood estimation of bivariate logistic models for incomplete responses with indicators of ignorable and non-ignorable missingness

Missing observations are a common problem that complicate the analysis of clustered data. In the Connecticut child surveys of childhood psychopathology, it was possible to identify reasons why outcomes were not observed. Of note, some of these causes of missingness may be assumed to be ignorable, whereas others may be non-ignorable. We consider logistic regression models for incomplete bivariate binary outcomes and propose mixture models that permit estimation assuming that there are two distinct types of missingness mechanisms: one that is ignorable; the other non-ignorable. A feature of the mixture modelling approach is that additional analyses to assess the sensitivity to assumptions about the missingness are relatively straightforward to incorporate. The methods were developed for analysing data from the Connecticut child surveys, where there are missing informant reports of child psychopathology and different reasons for missingness can be distinguished.