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Variants of non-symmetric correspondence analysis for nominal and ordinal variables

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Abstract

Non-symmetric correspondence analysis (NSCA) is a multivariate data analysis technique that has gained increasing attention in recent years. NSCA is an extension of traditional correspondence analysis that allows for the analysis of asymmetric association between two or more categorical variables. NSCA involves graphically depicting the one-way relationship between variables cross classified in a contingency table through a biplot. This paper provides a comprehensive overview of the popular approaches of NSCA developed over the years. Some fundamental variations in the family of NSCA such as Simple NSCA, Doubly Ordered NSCA, Singly Ordered NSCA, Three-way Nominal NSCA, Triply Ordered NSCA etc. are discussed thoroughly. A systematic step-by-step algorithms for each variant of NSCA and their demonstrations are neatly presented. Further a summary of NSCA variants in literature, the concise tabular presentation of R-packages developed for variants of CA/NSCA and a collection of variety of datasets where NSCA is performed are the key features of the paper. Moreover, we compare and contrast the method of NSCA with multinomial logistic regression (MNLR) to discuss some disparities between both the approaches. The paper aims to provide the theoretical, practical and computational issues of NSCA in structured manner and to highlight the further challenges with reference to NSCA.

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Acknowledgements

We would like to thank the Referees for their constructive comments and suggestions, which improved the manuscript significantly.

Funding

The first author would like to thank Department of Science and Technology, New Delhi for providing financial support for this work through the Inspire Fellowship Program (vide letter DST/INSPIRE fellowship/IF200013).

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  1. Department of Statistics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India

    Riya R. Jain & Kirtee K. Kamalja

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  1. Riya R. Jain
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Correspondence to Kirtee K. Kamalja.

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Jain, R.R., Kamalja, K.K. Variants of non-symmetric correspondence analysis for nominal and ordinal variables. J. Korean Stat. Soc. (2024). https://doi.org/10.1007/s42952-023-00253-0

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