Abstract:
Motivation: Dependence of multivariate binary outcomes in longitudinal data is challenging to study. Dependence in binary responses can be
tested using different techniques. Marshall-olkin correlation coefficient and
logistic regression model are two of the popular techniques. However, these
approaches do not elucidate the true relationship between the predictors and
responses if the responses are correlated. Numerous studies have been per-
formed to test the dependence in binary responses either using conditional
or marginal probability models. The conditional and marginal approach provide inadequate or misleading results due to the use of only conditional or
marginal model.
Method: A generalized linear model (GLM) is proposed using both
conditional and marginal probabilities. This is an extended model of bi-
variate correlated binary responses to tri-variate correlated binary responses.
The link function of the GLM is used to test the dependence of response
variables.
Results: Marshall-olkin correlation coefficients and logistic regression
coefficients provide moderate correlation in the mobility index which implies
the dependence of response variables. The analysis of the proposed model
for both datasets implies that this dependence is statistically signifcant.
