Estimation and test of measures of association for correlated binary data

This paper provides the estimation and test procedures for measures of association in the correlated binary data. Several measures of association are proposed for bivariate Bernoulli data during the past decades but the estimation and test procedures for most of these measures are not developed yet. In this paper, the inferential procedures for the measures of association are demonstrated. The generalized linear model approach (GLM) is employed for bivariate Bernoulli variables and the measures of association are estimated and appropriate test procedures are suggested. An alternative to the quadratic exponential form (QEF) is proposed to improve the normalization process. In this paper, different methods of measuring association between bivariate Bernoulli variables are compared. For comparison, we use a simulation procedure which indicates that all the measures of association and their test procedures provide almost similar results. However, the GLM and the proposed alternative quadratic exponential form (AQEF) models display slightly better performance.