Joint analysis of preferences and drop out data in discrete choice

Choice data appear together with drop out data indicating if respondents completed the exercise. In case of non-completion, the choice sequences end at the tasks where the respondents exited the study. In the analysis of choice data, the focus is always on choices made while the drop out behavior is completely ignored. However, the choice making and the drop out process could be latently related. For instance, respondents who are more likely to drop out of the exercise could give less consistent choices throughout or just before they exit. In such cases, ignoring the drop out dimension could lead to biased or inefficient results. In this paper, we use shared random effects and covariate effects to model the association between a scaled multinomial logit model for the choices and two different models for the drop out component. Through simulations, we show that a joint model provides less biased and more precise estimates and its 95% credible intervals have better coverage for true parameter values.