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Dependence in multivariate binary outcomes in longitudinal data is a challenging and an important issue to address. Numerous studies have been performed to test the dependence in binary responses either using conditional or marginal probability models. Since the conditional and marginal approach provide inadequate or misleading results, the joint models based on both are implemented for bivariate correlated binary responses. In the current paper, we consider a joint modeling approach and a generalized linear model (GLM) for tri-variate correlated binary responses. The link function of the GLM is used to test the dependence of response variables. The mobility index with two categories, no difficulty and difficulty, over the duration of three waves of Health and Retirement Survey (HRS) is chosen as the binary response variable. Initial analysis with Marshall-Olkin correlation coefficients and logistic regression coefficients provide moderate correlation in mobility indices implying dependence in the response variables. We also found statistically significant dependence among the response variables using the joint modeling approach. The mobility at current wave not only depends on the previous mobility status, but also depends on covariates such as age, gender, and race.

A generalized linear model for multivariate correlated binary response data on mobility index