Article

Nonlinear structural equation modeling: is partial least squares an alternative?

AStA Advances in Statistical Analysis (impact factor: 0.44). 04/2012; 94(2):167-184. DOI:10.1007/s10182-010-0132-3 pp.167-184

ABSTRACT Nonlinear structural equation modeling provides many advantages over analyses based on manifest variables only. Several approaches
for the analysis of latent interaction effects have been developed within the last 15 years, including the partial least squares
product indicator approach (PLS-PI), the constrained product indicator approach using the LISREL software (LISREL-PI), and
the distribution-analytic latent moderated structural equations approach (LMS) using the Mplus program. An assumed advantage
of PLS-PI is that it is able to deal with very large numbers of indicators, while LISREL-PI and LMS have not been investigated
under such conditions. In a Monte Carlo study, the performance of LISREL-PI and LMS was compared to PLS-PI results previously
reported in Chin et al. (2003) and Goodhue et al. (2007) for identical conditions. The latent interaction model included six indicator variables for the measurement of each latent
predictor variable and the latent criterion, and sample size was N=100. The results showed that PLS-PI’s linear and interaction parameter estimates were downward biased, while parameter estimates
were unbiased for LISREL-PI and LMS. True standard errors were smallest for PLS-PI, while the power to detect the latent interaction
effect was higher for LISREL-PI and LMS. Compared to the symmetric distributions of interaction parameter estimates for LISREL-PI
and LMS, PLS-PI showed a distribution that was symmetric for positive values, but included outlying negative estimates. Possible
explanations for these findings are discussed.

KeywordsNonlinear structural equation modeling-Interaction effect-Monte Carlo study-Partial least squares-LISREL-LMS

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Keywords

analyses
 
assumed advantage
 
constrained product indicator approach
 
distribution-analytic latent moderated structural equations approach
 
identical conditions
 
interaction parameter estimates
 
large numbers
 
last 15 years
 
latent criterion
 
latent interaction effects
 
latent interaction model
 
LISREL software
 
Monte Carlo study
 
Nonlinear structural equation modeling
 
outlying negative estimates
 
PLS-PI results
 
positive values
 
product indicator approach
 
symmetric distributions
 
True standard errors
 

Karin Schermelleh-Engel