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Regression, Discrimination and Measurement Models for Ordered Categorical Variables

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  • J. A. Anderson
  • P. R. Philips

Abstract

Regression models for the analysis of ordered categorical variables are discussed with particular reference to the logistic model. Maximum likelihood estimation procedures are established for three common sampling plans including the case where sampling is conditional on the ordered variable. This was previously not available. The use of these models in discrimination is discussed and an example given. An original method for the establishment of rating scales based on a coarse direct assessment and related variables is introduced. Mention is made of some difficulties in the application of the models and of their potential use for the analysis of designed experiments with ordered response variables.

Suggested Citation

  • J. A. Anderson & P. R. Philips, 1981. "Regression, Discrimination and Measurement Models for Ordered Categorical Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(1), pages 22-31, March.
    • Handle: RePEc:bla:jorssc:v:30:y:1981:i:1:p:22-31
    DOI: 10.2307/2346654
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    Cited by:

    1. Eleni Matechou & Ivy Liu & Daniel Fernández & Miguel Farias & Bergljot Gjelsvik, 2016. "Biclustering Models for Two-Mode Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 611-624, September.
    2. Gerhard Tutz, 2022. "Ordinal Trees and Random Forests: Score-Free Recursive Partitioning and Improved Ensembles," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 241-263, July.
    3. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    4. Verwaeren, Jan & Waegeman, Willem & De Baets, Bernard, 2012. "Learning partial ordinal class memberships with kernel-based proportional odds models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 928-942.
    5. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    6. Garcia, Alexis Arthur B. & Rejesus, Roderick M. & Genio, Emmanuel L., 2008. "Factors Influencing Artisanal Fisherfolks' Level of Support for Fishery Regulations: An Approach Using Alternative Ordered Logit Models," 2008 Annual Meeting, February 2-6, 2008, Dallas, Texas 6791, Southern Agricultural Economics Association.
    7. 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.
    8. Arooma Maryam & Sadia Aslam & Sidra Saif & Tehzeeb Aslam & Kishver Tusleem & Muhammad Tahir ul Qamar & Imran Abdullah & Atifa Mushtaq & Rana Rehan Khalid & Abdul Rauf Siddiqi, 2017. "Statistical Analysis Of Risk Factors Affecting The Prognosis Of Biliary Atresia In Infants," Matrix Science Pharma (MSP), Zibeline International Publishing, vol. 1(2), pages 20-24, September.
    9. 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.
    10. Alan Agresti & Claudia Tarantola, 2018. "Simple ways to interpret effects in modeling ordinal categorical data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 210-223, August.
    11. Melody S. Goodman & Yi Li & Anne M. Stoddard & Glorian Sorensen, 2014. "Analysis of ordinal outcomes with longitudinal covariates subject to missingness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 1040-1052, May.
    12. Diao Guoqing & Ning Jing & qin jing, 2012. "Maximum Likelihood Estimation for Semiparametric Density Ratio Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, June.

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