Evaluation of Test Statistics for Robust Structural Equation Modeling with Nonnormal Missing Data

The two-stage robust procedure for structural equation modeling with nonnormal missing data was developed, where the saturated mean vector and covariance matrix are obtained by robust M-estimators in the first stage and the robust estimates of means and covariances are then fittedby the structural model in the second stage. Several test statistics have been used to evaluate the two-stage robust method. Although theperformance of those test statistics for complete data has been evaluated and compared in the literature, their properties for incomplete nonnormal data have never been studied. This article aims to systematically evaluate and compare five test statistics, including the naive test statistic derived from normal-distribution-based maximum likelihood,a rescaled chi-square statistic, an adjusted chi-square statistic,a corrected residual-based asymptotical distribution free chi-square statistic, and a residual-based F-statistic. These statistics areevaluated under a linear growth curve model by varying eight factors: data distributions, missing data mechanisms, missing rates, samplesizes, numbers of measurement occasions, covariances between latent intercept and slope, variances of measurement errors, and downweight rates of the two-stage robust method. When the missingness exists, the test statistic derived from the two-stage normal-distribution-based maximum likelihood performs worse than the other four test statistics. Application of the two-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test (PIAT) mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort.