An Alternating Estimation Approach to Combine Optimal Scaling and SEM

• Activity Number: 534
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Patrick Mair*+ and Jan De Leeuw and Peter M. Bentler
• Companies: WU Vienna University of Economics and Business and University of California, Los Angeles and University of California, Los Angeles
• Keywords: optimal scaling ; structural equation modeling ; correlational aspect

Abstract

In areas such as the social sciences, data are commonly available on an ordinal or nominal scale level. If the method of analysis is structural equation modeling (SEM), researchers typically use polychoric correlations that assume underlying normality. We present an approach that avoids the use of polychoric correlations. It uses the technique of optimal scaling which rescales the values of (categorical) variables in an optimal way with respect to their scale levels. The SEM parameter estimation and the optimal scaling transformations are carried out in an alternating way: We start with a correlation matrix and fit a correlation structure model using the multinormal log-likelihood to find the structural parameters. Then we optimize the transformations using a so-called aspect function. Afterwards we fit a correlation structure model on the new correlation matrix, and so on.