A Direct Estimation Method on Analyzing Ipsative Data With Chan and Bentler's (1993) Method

Abstract

Ipsative data (individual scores subject to a constant-sum constraint), suggested to minimize response bias, are sometimes observed in behavioral sciences. Chan and Bentler (1993, 1996) proposed a method to analyze ipsative data in a single-group case. Cheung and Chan (2002) extended the method to multiple-group analysis. However, these methods require tedious procedures on formulating within- and between-group constraints and recovering the parameter estimates and their standard errors. A direct estimation method, which is equivalent to Chan and Bentler's method with an alternative model specification, is proposed in this article. The 1st-order factor-analytic ipsative model in Chan and Bentler's method is reparameterized as a restricted 2nd-order factor-analytic model with fixed factor loading matrix reflecting the ipsative properties in the direct estimation method. The direct estimation method can be easily extended to test measurement invariance properties in multiple-group analysis. Issues related to ipsative models are also addressed.