Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis

Abstract

Interest in considering nonlinear structural equation models is well documented in the behavioral and social sciences as well as in the education and marketing literature. This article considers estimation of polynomial structural models. An existing method is shown to have a limitation that the produced estimator is inconsistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estimator is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are discussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Application of the new procedure in a substance abuse prevention study is also reported.

The influence of stadium environment on attendance intentions in spectator sport

“…Using a LMS model, the present study tested the interaction effects of loyalty based on the intended conceptualization suggested by Wakefield and Sloan (1995). LMS was used to test the moderation effect because of its statistical rigor and robustness to nonnormality (Klein and Moosbrugger, 2000;Klein and Muthén, 2007) compared to conventional methods in estimating latent variable interactions (e.g., Bollen, 1996;Marsh et al, 2004;Ping, 1996;Wall and Amemiya, 2001).…”

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

“…If the original measures are severely non-normal, then the actual variances and covariances can be very different from the values implied by the constraints (Rigdon et al, 1998) and estimates can be biased (Wall and Amemiya, 2001). Fortunately, constraints (20) and (21) are not necessary for identification, even in the single indicator case.…”

Heteroscedastic factor analysis

“…This method was subsequently adopted by several other researchers investigating similar problems, including Jaccard and Wan (1995), Joreskog and Yang (1996), Ping (1996), Joreskog and Yang (1997), and Wall and Amemiya (1998). Our problem is not directly related to the polynomial latent variable model discussed in the literature.…”

“…One recent development in factor analysis and related fields is the use of a model where the relationships between factors and observed variables are nonlinear. See, for example, Kenny and Judd (1984), Ping (1996), Joreskog and Vang (1996), Joreskog eind Yang (1997), and Wall and Amemiya (1998). In this dissertation, we consider model (1.3) with possible dependency among ft, €it, ..., Cpj.…”