Multiple Correspondence Analysis and Orthonormal Principal Component Analysis:Analysis of a Survey of Professional Baseball Spectators

Abstract

Social survey questionnaires tend to be large numbers of items with diverse content. Hence, irrespective of the quantification procedure used, the quantitative dimensions obtained may be quite large. In the usual applications of multiple correspondence analysis (MCA), however, three-dimensional solutions are the most complex interpretations typically employed. Orthonormal principal component analysis (OPCA) for categorical variables (Murakami, 2020) was devised to interpret large-dimensional quantities of information in categorical variables. In this study OPCA is applied to survey data obtained from spectators at a Japanese professional baseball stadium. Six interpretable components are derived, and mean differences of component scores among four demographic groups are found. From the simple structure attained by rotation of the matrix of weights, it became possible to draw scatter plots between specified components. A few plots between uncorrelated but nonlinearly related components suggested that so-called horseshoe phenomena are not necessarily mathematical artifacts but may reflect empirical properties. MCA 1) 49 2) JSPS JP20K03303