Estimation of Regression to the mean for the Bivariate Generalized Poisson Lindley Distribution

Abstract

Regression to the mean (RTM) occurs when measurement/observations tends toward the mean of the population upon re-measurement . In pre-post studies interventions are applied to subj ects based on some cut-off points or baseline criteria. The change in the difference of the pre-post means after the application of an intervention is known as the total effect which is the sum of RTM and intervention effects. The total effect needs to be accounted for the RTM effect to unbiasedly estimate the intervent ion effe ct. In this work, we have derived the RTM effect for bivariate generalized Poisson lindley distribution with a particular emphasis on positive correlated count variables. Expressions for t he total effect are derived for a model and then partitioned into RTM and intervention effect. Maximum likelihood estimators are derived and its properties are verified via simulations. Finally, using the bivariate accident count data of 122 shunters, RTM and intervention effect are estimated.