Multiple taxicab correspondence analysis

Abstract

We compare the statistical analysis of multidimensional contingency tables by multiple correspondence analysis (MCA) and multiple taxicab correspondence analysis (MTCA). We will show in this paper: First, MTCA and MCA can produce different results. Second, taxicab correspondence analysis of a Burt table is equivalent to centroid correspondence analysis of the indicator matrix. Third, along the first principal axis, the projected response patterns in MTCA will be clustered and the number of cluster points is less than or equal to 1+ the number of variables. Fourth, visual maps produced by MTCA seem to be clearer and more readable in the presence of rarely occurring categories of the variables than the graphical displays produced by MCA. Two well known data sets are analyzed.