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A Unified Framework for the Comparison of Treatments with Ordinal Responses

Published online by Cambridge University Press:  01 January 2025

Tong-Yu Lu ,
Wai-Yin Poon  and
Siu Hung Cheung
Tong-Yu Lu*
Affiliation:
China Jiliang University
Wai-Yin Poon
Affiliation:
The Chinese University of Hong Kong
Siu Hung Cheung
Affiliation:
The Chinese University of Hong Kong
*
Requests for reprints should be sent to Tong-Yu Lu, College of Economics and Management, China Jiliang University, Hangzhou, China. E-mail: lutongyu@cjlu.edu.cn
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Abstract

Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustrate the proposed methods.

Keywords

latent variable modellocation-scale familyordinal responses
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 4 , October 2014 , pp. 605 - 620
Copyright
Copyright © 2013 The Psychometric Society

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