The Covariance Structure Analysis of Ipsative Data

Abstract

Data are called ipsative if they are subject to a constant-sum constraint for each observation. Usually, ipsative data are the consequence of transformation of their corresponding preipsative data. In this article, two kinds of ipsative data are defined. They are the additive ipsative data (AID) and the multiplicative ipsative data (MID). Jackson and Alwin proposed a method to analyze AID in exploratory factor analysis. However, they failed to provide the estimates of the original factor loadings. In this study, first, their method is modified in the context of covariance structure analysis. It is discovered that the original parameter estimates can usually be recovered provided the model of the preipsative data is well defined. An artificial example is used to demonstrate the suggested method. Second, the method is extended to the case of MID. A real example is considered also. Finally, some related issues, problems, and generalizations are addressed and discussed.