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Sources of heterogeneity in distributions with ordered categorical variables

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  • Wai-Yin Poon

Abstract

The chi-squared statistic is used to test the homogeneity for several groups in a contingency table. However, it may be inappropriate to apply the test when ordinal categories are involved. If it can be assumed that the ordinal categorical variables are realizations of underlying continuous random variables, then it is possible to study the properties of different groups in a relative sense. Assuming that the distributions of the continuous variables are in the same family and that the thresholds that define the categories are invariant across groups, we propose a procedure to test homogeneity and to address the sources of heterogeneity in different groups. An example based on a real data set is used to demonstrate the practical applicability of the suggested method.

Suggested Citation

  • Wai-Yin Poon, 1999. "Sources of heterogeneity in distributions with ordered categorical variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 383-392.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:3:p:383-392
    DOI: 10.1080/02664769922485
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    1. Ulf Olsson, 1979. "Maximum likelihood estimation of the polychoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 443-460, December.
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    1. Tang, Man-Lai & Poon, Wai-Yin, 2007. "Statistical inference for equivalence trials with ordinal responses: A latent normal distribution approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5918-5926, August.

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