Regression to the mean effect for bi-variate dispersed count data

Abstract

Regression to the mean (RTM) occurs when extreme observations upon remeasurement are found closer to the population mean. Interventions are usually applied to subjects based on a cut-off point to check it effectiveness. The average difference of the pre-post observations called the total effect is the sum of RTM and intervention effects and needs to be accounted for RTM to avoid incorrect conclusions and unbiasedly estimate the intervention effect. The existing methods assume equidispersion and strict positive correlation for bivariate count data. This study considers a bivariate Poisson distribution which takes both the dispersion and negative correlation into consideration. Expressions for the total effect are derived and partitioned into RTM and intervention effects. The maximum likelihood estimators of the RTM and intervention effects are found numerically, and their asymptotic properties are verified via simulations. Data on the English premier league are used to estimate the RTM and intervention effects.