Ordered categorical data frequently arise in the analysis of biomedical, agricultural and social sciences data. Sometimes categories are the result of grouping continuous data and produce ordered categorical responses. The ordered responses may be clustered and the subjects within the clusters may be positively correlated. A commonly used method to accommodate this correlation is to add a random component to the linear predictor of each clustered response. This article presents and compares latent variable random-effects models for analyzing ordered categorical data that are result of grouping continuous data. We present a general model that includes probit, logistic, complementary log-log and log-log models as its special cases. This model explains two sources of variation, between-cluster variation and within-cluster variation. The proposed models are applied to an agricultural experiment and a clinical trial data. Our results show that the random-effects models perform better than homogeneous models. We also show that the interpretation of the treatment effect depends on the choice of the probability model.

ordered categorical data, latent variable, random-effects, probit model, logit model, complementary log-log model, log-log model.