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On the bivariate normal distribution and association models for ordinal categorical data

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  • Becker, Mark P.

Abstract

The uniform association model and a linear-by-linear association model with "normal scores" are compared to probability distributions generated by partitioning the bivariate normal distribution. The association models are shown to be indistinguishable from their respective bivariate normal models when the dimensions of the contingency table are large. Exact calculations are used for making comparisons in small tables.

Suggested Citation

  • Becker, Mark P., 1989. "On the bivariate normal distribution and association models for ordinal categorical data," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 435-440, October.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:5:p:435-440
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    Citations

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    Cited by:

    1. Raymond Sin-Kwok Wong, 1994. "Model Selection Strategies and the Use of Association Models to Detect Group Differences," Sociological Methods & Research, , vol. 22(4), pages 460-491, May.
    2. Alessandro Barbiero & Asmerilda Hitaj, 2020. "Goodman and Kruskal’s Gamma Coefficient for Ordinalized Bivariate Normal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 905-925, December.
    3. Yuchung Wang, 1997. "Multivariate normal integrals and contingency tables with ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 267-284, June.
    4. Anderson, Carolyn J. & Li, Zhushan & Vermunt, Jeroen K., 2007. "Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i06).
    5. Eshima, Nobuoki, 2004. "Canonical exponential models for analysis of association between two sets of variables," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 135-144, January.
    6. Lapp, Krista & Molenberghs, Geert & Lesaffre, Emmanuel, 1998. "Models for the association between ordinal variables," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 387-411, October.
    7. Carolyn Anderson & Hsiu-Ting Yu, 2007. "Log-Multiplicative Association Models as Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 5-23, March.
    8. Anestis Touloumis & Alan Agresti & Maria Kateri, 2013. "GEE for Multinomial Responses Using a Local Odds Ratios Parameterization," Biometrics, The International Biometric Society, vol. 69(3), pages 633-640, September.
    9. repec:jss:jstsof:20:i06 is not listed on IDEAS

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