Estimation for Polynomial Structural Equation Models

Abstract

Structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing. Subject matter needs for considering nonlinear structural models have been well documented. But current fitting procedures are available only for a limited class of models. In this article a systematic statistical approach is developed for the general polynomial structural equation model. The new procedure applies a method of moments procedure similar to the one used in errors-in-variables regression to the factor score estimates from the measurement model fit. The asymptotic properties of the estimator are derived, and a modified estimator with better small-sample properties is introduced. Simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods. An example from a substance abuse prevention study is also discussed.

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

“…The limited information approach is adopted here. The general framework of structural equation modelling includes models for continuous variables, categorical variables, and mixtures of variables (Arminger & Küsters, 1988;Muthén, 1984), confirmatory factor analysis (Jöreskog, 1969), mixed effects analysis (Fan & Hancock, 2012), multi-group analysis (Jöreskog, 1971;Muthén, 1989), latent growth curve analysis (Bollen & Curran, 2006), and non-linear models (Jöreskog & Yang, 1996;Wall & Amemiya, 2000) as special cases. Estimation and testing remain important research topics when models involve non-normally distributed observed variables such as ordinal variables.…”

Firm Sustainability Performance Index Modeling

“…These include but are not limited to: (i) CSEM analysis with categorical data [29][30][31]; (ii) linear or nonlinear CSEM with covariates [32,33]; (iii) CSEM with nonlinear correlation [34,35], (iv) CSEM with multilevel dimensions [36][37][38]; (v) mixtures of CSEM [39,40]; (vi) CSEM with exponential indicators [41], (vii) CSEM with multi-sample [42,43], and (viii) CSEM with missing data [44,45].…”

Simple, Efficient and Distribution-free Approach to Interaction Effects in Complex Structural Equation Models

“…5. Some recent alternative approaches include the Bayesian approach of Arminger and Muthén (1998) the two-step method of moments approach of Wall and Amemiya (2000), and the quasi maximum likelihood estimation method (Klein and Muthén, Quasi maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Submitted to Multivariate Behavioral Research).…”