robustsem

Robustsem is a term used to describe robust structural equation modeling, a set of techniques designed to produce reliable parameter estimates and inference in SEM when classical assumptions are violated. Traditional structural equation modeling relies on multivariate normality and homoscedasticity; when data depart from these assumptions, standard maximum-likelihood estimates and chi-square tests can be biased. RobustSEM methods use estimation procedures and test statistics that are less sensitive to outliers, non-normality, and heteroskedasticity.

Common approaches include robust maximum likelihood estimation (RML) and sandwich-type standard errors, along with scaled test statistics such as the Satorra-Bentler and Yuan-Bentler corrections. Diagonally weighted or robust weighted least squares (DWLS, WLSMV) are often used for ordinal data or indicators with strong non-normality. Bootstrapping is also widely employed to obtain empirical standard errors and confidence intervals.

In practice, robustSEM is implemented in major SEM software, notably lavaan in R, which offers estimators like MLR (robust maximum likelihood) and related fit statistics; Mplus and EQS provide similar robust options; DWLS/WLSMV is common for ordinal indicators. Researchers typically report robust standard errors, robust test statistics, and robust fit indices in place of classical chi-square, RMSEA, CFI, etc., or supplement them with bootstrap-based intervals.

Applications span psychology, education, social sciences, marketing, and organizational research, particularly when data exhibit skewness, heavy tails, or contain outliers, or when sample sizes are modest. RobustSEM also supports measurement invariance testing under non-ideal conditions.

Limitations include potential efficiency loss when assumptions hold, sensitivity to model misspecification, and higher computational demands. Interpretation focuses on robust statistics and their bootstrap or sandwich-based equivalents rather than traditional maximum-likelihood tests.