  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.
