Regression Analysis of Proportion Outcomes with Random Effects

Abstract

A regression method for proportional, or fractional, data with mixed effects is outlined, designed for analysis of datasets in which the outcomes have substantial weight at the bounds. In such cases a normal approximation is particularly unsuitable as it can result in incorrect inference. To resolve this problem, we employ a logistic regression model and then apply a bootstrap method to correct conservative confidence intervals. This paper outlines the theory of the method, and demonstrates its utility using simulated data. Working code for the R platform is provided through the package glmmboot, available on CRAN.