Estimating intracluster correlation for ordinal data

TL;DR

This paper introduces a method to accurately estimate intracluster correlation for ordinal data, specifically applied to iPhone-based hearing tests, demonstrating reduced bias with logistic and probit models.

Contribution

It proposes a novel approach using mixed effects ordinal models for intracluster correlation estimation, improving accuracy over traditional linear models.

Findings

Linear models introduce bias in ordinal data

Ordinal models reduce bias in intracluster correlation estimates

Higher reliability estimates with ordinal models for hearing data

Abstract

Purpose: In this paper we consider the estimation of intracluster correlation for ordinal data. We focus on pure-tone audiometry hearing threshold data, where thresholds are measured in 5 decibel increments. We estimate the intracluster correlation for tests from iPhone-based hearing assessment application as a measure of test/retest reliability. Methods: We present a method to estimate the intracluster correlation using mixed effects cumulative logistic and probit models, which assume the outcome data are ordinal. This contrasts with using a mixed effects linear model which assumes that the outcome data are continuous. Results: In simulation studies we show that using a mixed effects linear model to estimate the intracluster correlation for ordinal data results in a negative finite sample bias, while using mixed effects cumulative logistic or probit models reduces this bias. The estimated intracluster correlation for the iPhone-based hearing assessment application is higher when using the mixed effects cumulative logistic and probit models compared to using a mixed effects linear model. Conclusion: When data are ordinal, using mixed effects cumulative logistic or probit models reduces the bias of intracluster correlation estimates relative to using a mixed effects linear model.