semTests

An R package for robust tests of overall fit and nested model comparisons in structural equation models. It works with lavaan and implements the penalized eigenvalue block averaging and penalized regression p values of Foldnes, Moss, and Grønneberg (2025), along with their extension to nested model comparison in Foldnes, Grønneberg, and Moss (2026).

It covers ML, GLS, ULS, categorical DWLS and ULS, and continuous FIML with one or several groups, for both single models and nested comparisons. Observed predictors are supported under joint random-x inference. See ?semTests-support for the exact list.

Installation

Install the released version from CRAN:

install.packages("semTests")

Or try the development version:

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

Examples

Here is a quick CFA:

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, tests = c("SB", "SS", "PEBA4"))
#>       sb_rls       ss_rls    peba4_rls
#> 1.726558e-07 9.251198e-07 5.165712e-07
#> estimator: ML (MLM) | data: continuous | information: expected | df: 24

For a nested comparison, pass 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, tests = c("SB", "SS", "PEBA2"))
#>     sb_rls     ss_rls  peba2_rls
#> 0.01023556 0.01092401 0.01051737
#> estimator: ML (MLM) | data: continuous | information: expected | df: 2 | nested (method 2000)

The fits need to use the same data, estimator, and fitting choices. If they arrive in the wrong order, semTests lets you know and swaps them.

Missing values are fine too. Fit the model with missing = "fiml" and call pvalues() as usual. semTests uses observed information by default, following Savalei (2010). The FIML vignette explains this choice and shows the other options.

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
#> 3.301286e-07
#> estimator: ML (MLR) (FIML) | data: continuous | information: observed | df: 24 | FIML convention: observed

Ordered indicators work in much the same way:

HSord <- lavaan::HolzingerSwineford1939
ordered_names <- paste0("x", 1:9)
HSord[ordered_names] <- lapply(
  HSord[ordered_names],
  function(x) ordered(cut(x, 3))
)
fit_ordinal <- lavaan::cfa(model, HSord, ordered = ordered_names)
pvalues(fit_ordinal)
#>     peba4_ml
#> 7.156389e-06
#> estimator: DWLS (WLSMV) | data: categorical | information: expected | df: 24

More examples

• vignette("continuous-data", package = "semTests")
• vignette("categorical-data", package = "semTests")
• vignette("fiml-missing-data", package = "semTests")
• vignette("latent-growth", package = "semTests")
• vignette("measurement-invariance", package = "semTests")
• vignette("semTests", package = "semTests")

The help page ?semTests-support gives the exact supported combinations.

References

Foldnes, N., Moss, J., & Grønneberg, S. (2025). Improved goodness of fit procedures for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 32(1), 1–13.

Foldnes, N., Grønneberg, S., & Moss, J. (2026). Penalized eigenvalue block averaging: Extension to nested model comparison and Monte Carlo evaluations. Behavior Research Methods, 58, article 107.

Savalei, V. (2010). Expected versus observed information in SEM with incomplete normal and nonnormal data. Psychological Methods, 15(4), 352–367.

How to Contribute or Get Help

Found a bug or have an idea? Open a GitHub issue. Pull requests are welcome too.