Regression Analysis of Proportion Outcomes with Random Effects

TL;DR

This paper introduces a logistic regression approach with bootstrap correction for analyzing proportional data with mixed effects, especially when outcomes cluster at bounds, improving inference accuracy.

Contribution

It presents a novel method combining logistic regression and bootstrap correction for fractional data with random effects, addressing limitations of normal approximation.

Findings

Method performs well on simulated data

Bootstrap correction improves confidence interval accuracy

Applicable for datasets with boundary-heavy outcomes

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.