Joint analysis of longitudinal count and binary response data in the presence of outliers

In this article, we develop an innovative, robust method for jointly analyzing longitudinal count and binary responses. The method is useful for bounding the influence of potential outliers in the data when estimating the model parameters. We use a log-linear model for the count response and a logistic regression model for the binary response, where the two response processes are linked through a set of association parameters. The asymptotic properties of the robust estimators are briefly studied. The empirical properties of the estimators are studied based on simulations. The study shows that the proposed estimators are approximately unbiased and also efficient when fitting a joint model to data contaminated with outliers. We also apply the proposed method to some real longitudinal survey data obtained from a health study.