GENERALISED BERNOULLI MODEL FOR CORRELATED BINARY RESPONSES: APPLICATION TO THE NATIONAL INCOME DYNAMICS STUDY (NIDS) DATASETS

ABSTRACT The bivariate Bernoulli model was used to estimate covariate parameters for conditional as well as marginal models for the NIDs datasets. This is a follow- up research on one conducted by Islam et al. (2012) which introduced the use of the bivariate Bernoulli model to properly specify the dependence among bivariate binary responses. The covariate parameters were estimated by first expressing the proposed model in the exponential family form, finding the log-likelihood function and then the corresponding estimating equations. The Newton Rahpson and the Nelder Mead methods of iteration were used to estimate the covariate parameters. The research revealed that the bivariate Bernoulli model fitted bivariate binary response data significantly better than the conditional logistic and the Generalized Estimating Equation (GEE) logistic models-marginal model. The result was same for both artificial and real-life data. It is worth mentioning that to aim at more efficient covariate estimates, the bivariate Bernoulli model is highly recommended for bivariate binary response data. However, further research is needed to choose an initial value when using the Newton Rahpson and the Nelder Mead methods of iteration, because it posed a serious challenge in this study. Again further research is recommended to probably use the multivariate Bernoulli distribution to fit multivariate binary response data and estimate covariate coefficients.