Multiple and multiway correspondence analysis

Abstract

One of the most popular, and versatile, ways of visually analyzing the associating between categorical data is to perform a correspondence analysis on the contingency table that is formed from their cross‐classification. Traditionally the analysis of multiple categorical variables involves transforming such a table into a two‐way form through “flattening,” stacking or by some other means; doing so leads to simple or multiple correspondence analysis. Although such a transformation does not always preserve some of the truly multivariate nature of the association. Therefore one may instead adopt the less common multiway correspondence analysis. This paper will briefly explore the development, literature, and possible research opportunities of multiple and multiway correspondence analysis. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction Data: Types and Structures > Categorical Data

Exploring the association between self-efficacy and future utility beliefs in mathematics: A practical tutorial on correspondence analysis

“…While attention in this paper has been confined to examining the association between two variables ( Utility and Efficacy ) there are clearly other factors that impact upon them both, including gender, socio-economic background and parental/family influences. For such examinations, multiple and/or multi-way correspondence analysis [ 20 – 22 , 28 ] can be adapted to study educational data for future research. Doing so will provide an understanding of the role and influences of other factors on the association between the future utility of mathematics and self-assessed mathematics efficacy in the context of education research.…”

“…Therefore, SCA will be applied to Table 1 and can be viewed as a descriptive and exploratory statistical tool that is used to visually analyse the association between two categorical variables [19][20][21][22]. When a study consists of multiple categorical variables then multiple and multi-way correspondence analysis can be applied [28]. SCA has practical benefits including its ability to handle data that may not satisfy the necessary data restrictions used in statistical analysis techniques [37].…”

“…We highlight that confining our attention to just exploring the nature of the association between two educational variables may provide a limited perspective for some since covariate information concerning, for example, demographic information of the students or school type (public versus private), is not being considered in this study. Additional variables certainly can be taken into account although require multivariate versions of SCA, often referred to as multiple correspondence analysis (MCA) and multi-way correspondence analysis (MWCA); see [ 28 ] for a discussion of the key differences between these methods. Since this paper focuses on the application and practical interpretation of SCA for examining the association between Utility and Efficacy we shall consider the application using MCA or MWCA to the study of more variables for future consideration.…”

Multiple correspondence analysis as a tool for examining Nobel Prize data from 1901 to 2018

“…where X 2 qq0 is the chi-squared statistic for the (q, q 0 ) off-diagonal sub-matrix of C [21]. By adopting the terminology commonly used in correspondence analysis, the quantity X 2 /n is proportional to Pearson's chi-squared statistic and is referred to as the 'total inertia' of the contingency table; its components are referred to as 'principal inertias' that are often expressed as a percentage of the total inertia [22].…”

Symmetrical and Non-symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables

“…Kroonenberg (1996, 1998) and Kroonenberg (2008, Chapter 17) developed a comprehensive approach to deal with three-way categorical data, that is, three-way correspondence analysis, which includes the Lancaster partitioning of the chi-squared (and phisquared) statistic (Lancaster, 1951), modelling of the global dependence in the three-way table and graphing of the global dependence via three-way correspondence analysis. Rather than using three-way correspondence analysis, it is more usual to examine sets of two-way tables and employ multiple correspondence analysis to an indicator matrix or a Burt matrix (Benzécri, 1973, 1977, Greenacre, 1984, Chapter 5, Greenacre, 1990, 2017, Greenacre and Blasius, 2006, thereby ignoring higherorder associations among variables (Beh and Lombardo, 2019).…”