Structural Equation Modeling for Non-Normal Data in Marketing Research

• Activity Number: 17
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and Marketing
• Author(s): Junghun Nam*+ and Hamparsum Bozdogan
• Companies: University of Tennessee and University of Tennessee
• Keywords: structural equation model ; non-normal data ; information complexity ; elliptically contoured distribution

Abstract

The nature of marketing data is often non-normal. The non-normality appears in data structures such as satisfaction, loyalty, and service quality, to mention a few. Current SEM techniques used in the literature are all based on the assumption of normality. A very little attention has been given to the non-normality issues of the data sets at hand. This study, therefore, introduces a new technique to address the non-normality problems in SEM. This is achieved by considering a larger richer class of distributional models called the Elliptically Contoured (EC) distributions, where the normal distribution is just a sub-family. The recipe we utilize is to: obtain the parameter estimates and their covariance matrix under the normality assumption; compute the consistent estimator of the kurtosis parameter; and then scale the covariance matrix of the parameter estimates by kurtosis parameter when the random error is in fact EC distributed. Information complexity (ICOMP) criterion is developed to select the best-fitting SEM and is compared with Asymptotically Distribution Free method. Numerical and simulation examples are provided to illustrate the versatility of this new approach.