SatorraBentler

SatorraBentler commonly refers to the joint contribution of T. Satorra and P. M. Bentler, best known for developing the Satorra–Bentler scaled chi‑square statistic used in structural equation modeling (SEM). In their seminal 1994 paper, Satorra and Bentler addressed the problem of non‑normal data inflating chi‑square test statistics. They proposed a scaling correction that adjusts the test statistic to account for skewness and kurtosis, thereby providing a more accurate assessment of model fit when assumptions of multivariate normality are violated. The method estimates a scaling factor based on the observed fourth moments and applies it to the large‑sample chi‑square value derived from maximum likelihood estimation.

The Satorra–Bentler adjustment has become a standard tool in SEM software packages such as LISREL, AMOS, Mplus, and R’s lavaan package. It enables researchers to conduct fit tests on models estimated with non‑normal data without resorting to resampling methods like bootstrapping. In addition to the chi‑square correction, Satorra and Bentler published further refinements to the standard errors and test statistics of parameter estimates, enhancing overall inference in SEM.

Beyond the scaled chi‑square, Satorra and Bentler’s work has influenced the development of alternative fit indices, such as the robust comparative fit index (CFI) and robust root mean square error of approximation (RMSEA). Their research has been widely cited across fields that employ SEM, including psychology, sociology, economics, and education. The pair’s contributions are regarded as foundational in the application of SEM to real‑world data, where strict normality rarely holds, and have shaped contemporary best practices in model evaluation and inference.