Structural Equation Models of Latent Interactions: Evaluation of Alternative Estimation Strategies and Indicator Construction.

TLDR

Interactions between multiple indicator latent variables are rarely used because of implementation complexity and competing strategies. The authors compared general strategies for defining product indicators to represent the latent interaction factor. Simulation studies revealed that the traditional constrained approach performed worse than three new methods (unconstrained, generalized appended product indicator, and QML); the unconstrained method was easiest to apply, all approaches were unbiased with normally distributed indicators, but constrained and QML were more biased with nonnormal data, and QML offered higher power at the cost of increased Type I error rates.

Abstract

Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.