README

An R package for robust test statistics in structural equation models, covering both overall goodness of fit testing and nested model comparison. Built on top of lavaan. It implements the penalized eigenvalue block averaging and penalized regression p values of Foldnes, Moss, & Grønneberg (2024), together with their extension to nested model comparison in Foldnes, Grønneberg, & Moss (2026).

The eigenvalue correction targets the limiting null law of the test statistic, a weighted sum of chi squares. This law holds for any minimum discrepancy estimator, so support now reaches beyond normal theory ML to GLS, ULS, categorical WLSMV/DWLS, and FIML missing data fits. See ?semTests-support for the full validated matrix.

Installation

install.packages("semTests")

# install.packages("remotes")
remotes::install_github("JonasMoss/semTests")

Usage

Call the library function, create a lavaan model, and run the pvalues function.

library("semTests")
model <- "visual  =~ x1 + x2 + x3
          textual =~ x4 + x5 + x6
          speed   =~ x7 + x8 + x9"
object <- lavaan::cfa(model, lavaan::HolzingerSwineford1939, estimator = "MLM")
pvalues(object)
#>    peba4_rls 
#> 5.165737e-07 
#> estimator: ML | data: continuous | information: expected | df: 24

For nested model comparison, fit the constrained and unconstrained models and pass both to pvalues_nested, the constrained model first.

constrained <- "visual  =~ x1 + x2 + x3
                textual =~ a*x4 + a*x5 + a*x6
                speed   =~ x7 + x8 + x9"
m1 <- lavaan::cfa(model, lavaan::HolzingerSwineford1939, estimator = "MLM")
m0 <- lavaan::cfa(constrained, lavaan::HolzingerSwineford1939, estimator = "MLM")
pvalues_nested(m0, m1)
#> pall_ug_ml 
#>  0.0166158 
#> estimator: ML | data: continuous | information: expected | df: 2 | nested (method 2000)

Missing data is handled through full information maximum likelihood. Fit the model with missing = "fiml" and pass it to pvalues as usual. FIML uses the biased gamma and the standard statistic, so the UG/RLS suffixes do not apply.

HS <- lavaan::HolzingerSwineford1939
set.seed(313)
HS$x1[sample(nrow(HS), 60)] <- NA
fit_fiml <- lavaan::cfa(model, HS, missing = "fiml", estimator = "MLR")
pvalues(fit_fiml)
#>     peba4_ml 
#> 3.301171e-07 
#> estimator: ML (FIML) | data: continuous | information: observed | df: 24

References

Foldnes, N., Moss, J., & Grønneberg, S. (2024). Improved goodness of fit procedures for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 1–13. https://doi.org/10.1080/10705511.2024.2372028

Foldnes, N., Grønneberg, S., & Moss, J. (2026). Penalized eigenvalue block averaging: Extension to nested model comparison and Monte Carlo evaluations. Behavior Research Methods. https://doi.org/10.3758/s13428-026-02968-4

Foldnes, N., & Grønneberg, S. (2018). Approximating Test Statistics Using Eigenvalue Block Averaging. Structural Equation Modeling, 25(1), 101–114. https://doi.org/10.1080/10705511.2017.1373021

Du, H., & Bentler, P. M. (2022). 40-Year Old Unbiased Distribution Free Estimator Reliably Improves SEM Statistics for Nonnormal Data. Structural Equation Modeling: A Multidisciplinary Journal, 29(6), 872–887. https://doi.org/10.1080/10705511.2022.2063870

Marcoulides, K. M., Foldnes, N., & Grønneberg, S. (2020). Assessing Model Fit in Structural Equation Modeling Using Appropriate Test Statistics. Structural Equation Modeling, 27(3), 369–379. https://doi.org/10.1080/10705511.2019.1647785

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02

How to Contribute or Get Help

If you encounter a bug, have a feature request or need some help, open a Github issue. Create a pull requests to contribute.