Dependence in binary outcomes: a quadratic exponential model approach

Repeated measurements data appear in many applications of study subjects such as correlated binary data. Most of studies often focus on the dependence of marginal response probabilities. There is a lack of study based on joint probability distributions that yield estimation and test procedure using conditional probabilities, marginal means and correlated binary data. In this paper, the quadratic exponential form model has been extended for a Markov chain framework. This study extends the quadratic exponential model for displaying the estimation procedure for the nature and extent of dependence among the binary outcomes. In addition, a test procedure is extended to test for the goodness of fit of the model as well as for testing the order of the underlying Markov chain. The proposed model and the test procedures have been examined thoroughly with an application to elderly population data from the Health and Retirement Study (HRS) data.