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On exploratory analytic method for multi-way contingency tables with an ordinal response variable and categorical explanatory variables

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  • Wei, Zheng
  • Kim, Daeyoung

Abstract

In this paper, we propose a new model-free exploratory method for descriptive modeling that identifies and measures the regression dependence between an ordinal response variable and categorical (ordinal or nominal) explanatory variables in a multi-way contingency table. The proposed methodology consists of three parts, checkerboard copula score, checkerboard copula regression, and checkerboard copula association measure. The checkerboard copula score is a new type of score for ordinal variables that preserves the natural ordering of the categorical scale and it will be exploited for developing the methods measuring the association between the variables of interest. The checkerboard copula regression identifies the regression dependence between an ordinal response variable and categorical explanatory variables. It enables delineating the identified dependence in an exploratory manner. The checkerboard copula association measure quantifies the strength of the dependence identified by the checkerboard copula regression. We investigate the properties of checkerboard copula scores, checkerboard copula regression, its association measure, and their estimators. Finally, the performance of the proposed method is illustrated with simulation and real data.

Suggested Citation

  • Wei, Zheng & Kim, Daeyoung, 2021. "On exploratory analytic method for multi-way contingency tables with an ordinal response variable and categorical explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000713
    DOI: 10.1016/j.jmva.2021.104793
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    References listed on IDEAS

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    1. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    2. Li, Chun & Shepherd, Bryan E., 2010. "Test of Association Between Two Ordinal Variables While Adjusting for Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 612-620.
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    4. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2017. "Asymptotic behavior of the empirical multilinear copula process under broad conditions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 82-110.
    5. Lu Yang & Edward W. Frees & Zhengjun Zhang, 2020. "Nonparametric Estimation of Copula Regression Models With Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 707-720, April.
    6. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
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    Cited by:

    1. Wei, Zheng & Wang, Li & Liao, Shu-Min & Kim, Daeyoung, 2023. "On the exploration of regression dependence structures in multidimensional contingency tables with ordinal response variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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