Structural equation modeling relates latent factors, measured by observed indicators, to one another and to observed variables — covering CFA, path analysis and full SEM in one framework.
SEM combines a measurement model (latent factors defined by observed indicators, 'F1 =~ x1 + x2 + x3') with a structural model (regressions among latents and observed variables, 'F2 ~ F1 + age'). Confirmatory factor analysis is the special case with no structural part; path analysis the special case with no latents.
Estimation is (by default) maximum likelihood on the covariance matrix: the model implies a covariance structure, and the χ² statistic tests whether the observed covariances are consistent with it. Because χ² is sample-size sensitive, practice leans on approximate fit indices — CFI/TLI (incremental fit vs a null model), RMSEA (misfit per degree of freedom, with CI), and SRMR (average residual correlation).
Each latent factor needs an identification constraint; the model fixes the first indicator's loading to 1 by default (those rows show no SE/z/p). MLR provides robustness to non-normality; FIML uses all available data under missing-at-random instead of listwise deletion.
The computation runs entirely in your browser.
Numeric columns (column headers become variable names) + a model in the model syntax + estimator (ML / MLR / GLS) + missing-data handling (listwise / FIML).
Parameter table (loadings, regressions, covariances, variances) with SE / z / p / 95% CI / standardized estimates; fit indices (χ², CFI, TLI, RMSEA + CI, SRMR, AIC, BIC); R² per endogenous variable; convergence + post-check warnings.
Check convergence first, then fit: CFI/TLI ≥ 0.95, RMSEA ≤ 0.06, SRMR ≤ 0.08 (Hu & Bentler 1999) indicate good fit. Then read the standardized loadings (≥ 0.5 desirable) and structural paths like regression coefficients.