The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach

This article presents methods for analyzing the relationships among a set of qualitative variables when some of these variables are specified manifest (i.e., observed) variables and others are latent (i.e., unobserved or unobservable) variables. We shall show how to estimate the magnitude of the various effects represented in pathdiagram models that include both the manifestand latent variables, and also how to test whether this kind of path-diagram model is congruent with the observed data. These methods can be applied in order to analyze data obtained in various kinds of surveys (including panel studies), and also in order to construct tests and indices for purposes of measurement and prediction. To illustrate their wide applicability and flexibility, we shall use these methods to reanalyze several different sets of data which were analyzed earlier by Coleman (1964), Lazarsfeld (1948, 1970), Goodman (1973a), and others. Except for some related conclusions in Goodman (1973a), the methods introduced herein lead to conclusions that are very different from those presented by the other researchers who had analyzed these data earlier.