Theory and Methods of Statistics

12.12.3 Cross-Classified Data and Canonical Correlation

Consider the 5 × 5 contingency table given below on the occupational status of n = 3497 father-son pairs. Data sets of this type have been analyzed by many authors in order to investigate issues of intergenerational mobility. Note that occupational status is a qualitative variable and its numbering of 1 through 5 is purely descriptive. Can we assign numerical values for father’s and son’s status so that they can be treated as “quantitative” variables? This issue will be addressed here using canonical correlation analysis.

Suppose that we have an r × c contingency table with cell counts {n_ij} and the total is $n=\sum \sum n_{ij}$. For i = 1, …, r, and j = 1, …, c, create the following indicator variables, ...