Infant homicides: An examination using multiple correspondence analysis

Abstract

Multiple correspondence analysis (MCA) is a highly useful descriptive statistical technique that creates dimensional coordinates used to graphically display relationships among the attributes of multiple variables. It calculates row and column coordinates that are analogous to factors in a principal component analysis (PCA), differing from the latter in that it partitions the chi-square value instead of the total variance among variables. Although MCA is an excellent technique for examining large numbers of categorical variables, it has received little attention in social science research. Many social research variables are naturally discrete, as they are measured at the nominal level. Such variables are naturally displayed in contingency tables and well suited for analyses using the Pearson chi-square or the likelihood ratio chi-square, methods frequently used by social researchers. Both techniques work well for small tables, but they have limitations when tables contain many categorical variables that aggregate into a large number of combinations. Trying to interpret the resulting combinations can be a complex challenge. Correspondence analysis overcomes this diffi culty by calculating row and column coordinates—the “correspondence” between rows and columns— and partitioning the chi-square value into dimensions. A correspondence plot can then be produced to show the relationships between the row and column categories in a single visual.