WLSMV

WLSMV stands for Weighted Least Squares with Mean and Variance adjustment. It is an estimator used in structural equation modeling (SEM) when data are ordinal or otherwise non-normal. WLSMV is widely implemented in software such as Mplus and the lavaan package in R, where it is commonly applied to CFA and SEM with Likert-type items or other categorical outcomes.

Methodologically, WLSMV treats observed ordinal variables as discretized manifestations of underlying continuous latent responses. It relies on polychoric (and polyserial) correlations to summarize relationships among variables and uses a diagonally weighted least squares criterion to estimate model parameters. The diagonal weight matrix reduces computational burden, making the method practical for models with many indicators. Parameter estimates are obtained by minimizing the weighted discrepancy between the observed and model-implied correlation structure.

A key feature of WLSMV is its inference framework. It provides robust standard errors via a sandwich estimator and yields a mean- and variance-adjusted chi-square statistic for model fit, which improves Type I error control under non-normality. This adjustment also affects the distribution used for p-values, making the chi-square test statistic more accurate in typical SEM applications with ordinal data. Standard fit indices such as CFI, TLI, and RMSEA can be reported alongside these corrected statistics.

Strengths and limitations: WLSMV is well suited for ordinal data and non-normal distributions, offering robust standard errors and an adjusted chi-square test. It can be more stable and scalable than full information methods with categorical outcomes. Limitations include reliance on large-sample approximations for polychoric correlations and potential inefficiency relative to ML when data are truly continuous, as well as sensitivity to sparse categories.