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A Unified Framework for the Comparison of Treatments with Ordinal Responses

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  • Tong-Yu Lu
  • Wai-Yin Poon
  • Siu Cheung

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. Copyright The Psychometric Society 2014

Suggested Citation

  • Tong-Yu Lu & Wai-Yin Poon & Siu Cheung, 2014. "A Unified Framework for the Comparison of Treatments with Ordinal Responses," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 605-620, October.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:4:p:605-620
    DOI: 10.1007/s11336-013-9367-8
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    1. Rosa Maria Fanelli, 2021. "Barriers to Adopting New Technologies within Rural Small and Medium Enterprises (SMEs)," Social Sciences, MDPI, vol. 10(11), pages 1-15, November.
    2. Lu, Tong-Yu & Poon, Wai-Yin & Cheung, Siu Hung, 2016. "Multiple comparisons of treatments with skewed ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 223-232.
    3. Alan Agresti & Maria Kateri, 2017. "Ordinal probability effect measures for group comparisons in multinomial cumulative link models," Biometrics, The International Biometric Society, vol. 73(1), pages 214-219, March.

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