Modelling correlated ordinal data by random-effects logistic regression models: simulation and application

TL;DR

This paper introduces and compares random-effects logistic regression models for analyzing correlated ordinal data, demonstrating improved accuracy over homogeneous models through simulation and real data application.

Contribution

It proposes random-effects models for clustered ordinal data and shows their superiority over traditional homogeneous models in estimation accuracy.

Findings

Random-effects models fit data better statistically.

They estimate category probabilities more precisely.

Homogeneous models perform poorly in correlated data.

Abstract

Ordered categorical data frequently arise in the analysis of biomedical, agricultural, and social sciences data. The logistic regression model is attractive in analyzing ordered categorical data because of its use in interpretation of a parameter estimate. The ordered responses may be clustered and the subjects within the clusters may be positively correlated. To accommodate this correlation we add a random component to the linear predictor of each clustered response. This article presents and compares random-effects logistic regression models for analyzing ordered categorical data. The proposed models are applied to an agricultural experimental data. In order to assess the performance of the random-effects and homogeneous models we perform a simulation study. Our analysis, application to real data and simulation, show that the probability of the individual categories are estimated poorly in homogeneous models. The random-effects models fit the data statistically significant and estimate the probability of the individual categories more precisely.