A GENERALIZED LINEAR MODEL FOR MULTIVARIATE CORRELATED BINARY RESPONSE DATA ON MOBILITY INDEX

Abstract

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.