COMPARING LATENT INTERACTION EFFECTS IN MULTI-SAMPLE STRUCTURAL EQUATION MODELING: QUASI-MAXIMUM LIKELIHOOD VERSUS THIRD MOMENT METHODS

A simulation study was performed comparing the quasi-maximum likelihood (QML; Klein & Muthén, 2007) and third moment (Mooijaart & Bentler, 2010) methods for estimating latent interaction effects in multi-sample structural equation modeling. Both of these methods estimate latent interaction effects without the use of product indicators or the need to specify nonlinear constraints. The purpose of this study was to evaluate the power and type-I error rates for testing group differences of a latent interaction effect. This study also evaluated the parameter recovery of the two methods. A bootstrapping procedure was also proposed for the third moment method that tested the differences of empirical sampling distributions of interaction effects using a two-sample Kolmogorov-Smirnov test. There were four independent variables: i) sample size, ii) non-normality of errors, iii) effect size, and iv) estimation methods. \ud The QML method performed better than the third moment method. QML had lower type-I error and more power. QML had less absolute bias for estimating smaller interaction effects. For smaller sample sizes, QML had less error in estimating interaction effects, main effects and covariances than the third-moment method. The nonnormality conditions had no impact on the results. Based on the pattern of results found, it is recommended that QML method be used for testing if a latent interaction differs between groups. If the M-B method is to be used the sample size to parameter ratio should be greater than 20:1. Care should be taken in interpreting parameter estimates in the presence of a large interaction effect as both methods overestimated an interaction coefficient as it increased in magnitude. Both methods also had more error in estimating main effects and covariances as the interaction effect increased