Reexamining Nonlinear Structural Equation Modeling Procedures: The Effect of Parallel and Congeneric Measures

Abstract

The current study examines the performance of the extended unconstrained approach (EXUC) and the latent moderated structural equation modeling procedure (LMS) in situations where quadratic and interaction terms are tested simultaneously and investigates their limitations with regard to the employment of parallel and congeneric measures, relatively low indicator reliabilities, and relatively large numbers of indicators. By means of a Monte Carlo study, we found LMS to be the best option for testing multiple nonlinear effects given sufficient sample size (n ≥ 500) and normally distributed exogenous variables. Its advantages became more prominent when indicator reliabilities were heterogeneous and small. The EXUC was a viable option for estimating the model when indicators were parallel and exhibited large indicator reliabilities. An empirical example of the results is provided, and the relevance of measurement model characteristics to assess nonlinear relationships is discussed.

Effects of healthy aging and mnemonic strategies on verbal memory performance across the adult lifespan: Mediating role of posterior hippocampus

“…This approach needs medium to large sample size ( n > 500) for stable, unbiased effect estimations (Henseler & Chin, 2010). For example, the inclusion of product indicator for quadratic term requires dichotomizing continuous variables, which may lead to information loss and spurious interaction effects (Dimitruk et al, 2007), and a large sample size for robust and reliable nonlinear SEM models (Navarro & Alvarado, 2015).…”

Organizational Multichannel Differentiation: An Analysis of Its Impact on Channel Relationships and Company Sales Success

“…In doing so, the interaction terms of one indicator of the moderator and one indicator of the predictor serve as reflective indicators for measuring the latent interaction term on the construct level. As a rule for creating these interaction terms, studies advise against combining every indicator of the moderator with every indicator of the predictor, as this would, for example, lead to disproportionately high complexity of the model, but instead suggest applying the matched-pairs approach (Marsh, Wen, and Hau 2004, 2006; Rdz-Navarro and Alvarado 2015). According to this approach, each indicator should not be used more than once for creating matched pairs, thus keeping model complexity at a reasonable level but also ensuring that all measurement information is used.…”

The use of items and item parcels in nonlinear structural equation models

“…It has been demonstrated that LMS yields unbiased, efficient and consistent parameter estimates when the normality assumption of predictors is true (Jackman, Leite, & Cochrane, 2011;Kelava et al, 2011;Rdz-Navarro & Alvarado, 2015). However, because of the strong dependence of LMS on such an assumption, its properties may not remain true when predictors are not normal (Brandt, Kelava, & Klein, 2014).…”

“…First, continuous items (X i ) were generated for each factor according to a simple structure (i.e., cross-loadings = 0) and the model in Equation 3. For simplicity, the factor loadings were set to .5, a value which has shown reasonable results in previous studies (Rdz-Navarro & Alvarado, 2015). The measurement errors (δ i ) were generated from an N(0, 0.75) distribution, such that all X i follow an N(0, 1) distribution.…”