A survey of models for repeated ordered categorical response data

Area of Science:

• Biostatistics
• Statistical Modeling
• Longitudinal Data Analysis

Background:

• Repeated observations on ordered categorical variables are common in various scientific fields.
• Analyzing such data requires specialized statistical models that account for the nature of the response and the correlation between measurements.
• Existing methods may not fully capture the complex dependencies inherent in longitudinal categorical data.

Purpose of the Study:

• To survey and present statistical models for analyzing repeated observations on an ordered categorical response variable.
• To describe models that simultaneously account for explanatory variables and the occasion of response.
• To discuss methods for fitting these models, including maximum likelihood, weighted least squares, and semi-parametric approaches.

Main Methods:

• Univariate models allowing correlation among repeated measurements.
• Models based on three transformations of the response distribution: cumulative logits, adjacent-category logits, and mean scores.
• Discussion of fitting methods: maximum likelihood, weighted least squares (WLS), and semi-parametric techniques.

Main Results:

• The presented models effectively analyze ordered categorical response variables with repeated measures.
• Weighted least squares (WLS) is highlighted as a practical and easily implementable method, demonstrated using SAS.
• The models allow simultaneous examination of how explanatory variables and time influence response distributions.

Conclusions:

• The surveyed models provide a robust framework for analyzing longitudinal ordered categorical data.
• WLS offers a computationally feasible approach for fitting these complex models, facilitating their application in research.
• These methods are valuable for understanding treatment effects, as shown in the insomnia drug-placebo comparison example.