A COMPARISON OF LATENT INTERACTION ESTIMATORS—MODEL IMPLIED INSTRUMENTAL VARIABLES AND DISTRIBUTIONAL APPROACHES

Here the finite sample performance of several estimators of latent interaction effects were compared in a Monte Carlo simulation study which manipulated sample size, measurement model misspecification, latent variable nonnormality, indicator reliability, and number of indicators. These estimators include the model implied instrumental variables, generalized method of movements (MIIV-GMM), model implied instrumental variables, two-stage least squares (MIIV-2SLS), latent moderated structural equations (LMS), and quasi-maximum likelihood (QML) estimation approaches. The MIIV estimators showed no varied performance due to misspecification; low reliability was associated with higher relative bias. The LSM estimator showed under estimated standard errors that grew worse with nonnormality; QML showed bias in both its estimates and standard errors. The MIIV estimators typically had observed confidence interval rates closest to the nominal value. The LMS estimator typically showed the lowest mean squared error of the estimators when sample size was small or when reliability was low.