New Methods for Analyzing the Intrinsic Character of Qualitative Variables Using Cross-Classified Data

Abstract

This paper describes new methods for analyzing the intrinsic character of qualitative variables (variables pertaining to nominal attributes and/or to ordinal categorical classifications), using the observed cross-classification table pertaining to these variables. The new methods can be applied to determine whether the particular variables of interest can be expressed in intrinsic metric terms, using the pattern of the observed joint distribution of variables in a cross classification table as evidence pertaining to the possible intrinsic metric character of the variables. These methods are related to, but different from, (1) methods developed earlier in connection with Guttman's approach to scale analysis, (2) methods developed earlier in connection with Lazarsfeld's approach to latent-class analysis, and (3) methods developed more recently in connection with the loglinear approach. These three approaches appear, at first sight, to be very different from one another, but, with the introduction of the new methods described in the present paper, we shall be able to see more clearly how the three approaches are related to one another, and also how the new methods described here improve on the methods obtained with each of the three earlier approaches.