A generalized bivariate Bernoulli model with covariate dependence

Dependence in outcome variables may pose formidable difficulty in analyzing data in longitudinal studies. In the past, most of the studies made attempts to address this problem using the marginal models. However, using the marginal models alone, it is difficult to specify the measures of dependence in outcomes due to association between outcomes as well as between outcomes and explanatory variables. In this paper, a generalized approach is demonstrated using both the conditional and marginal models. This model uses link functions to test for dependence in outcome variables. The estimation and test procedures are illustrated with an application to the mobility index data from the Health and Retirement Survey and also simulations are performed for correlated binary data generated from the bivariate Bernoulli distributions. The results indicate the usefulness of the proposed method.