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Type: Package
Title: Goodness-of-Fit Testing for Structural Equation Models
Description: Supports eigenvalue block-averaging p-values (Foldnes, Grønneberg, 2018) <doi:10.1080/10705511.2017.1373021>, penalized eigenvalue block-averaging p-values (Foldnes, Moss, Grønneberg, 2024) <doi:10.1080/10705511.2024.2372028>, penalized regression p-values (Foldnes, Moss, Grønneberg, 2024) <doi:10.1080/10705511.2024.2372028>, as well as traditional p-values such as Satorra-Bentler. All p-values can be calculated using unbiased or biased gamma estimates (Du, Bentler, 2022) <doi:10.1080/10705511.2022.2063870> and two choices of chi square statistics.
Version: 0.7.1
License: GPL (≥ 3)
Encoding: UTF-8
URL: https://github.com/JonasMoss/semTests
Depends: R (≥ 3.5.0)
Imports: lavaan (≥ 0.6-16), CompQuadForm, RSpectra, MASS, Matrix, methods
Suggests: covr, testthat (≥ 3.0.0), psych
Config/testthat/edition: 3
RoxygenNote: 7.3.3
NeedsCompilation: no
Packaged: 2025-10-06 11:58:43 UTC; A2010578
Author: Jonas Moss ORCID iD [aut, cre], Njål Foldnes ORCID iD [ctb], Steffen Grønneberg ORCID iD [ctb]
Maintainer: Jonas Moss <jonas.moss.statistics@gmail.com>
Repository: CRAN
Date/Publication: 2025-10-09 12:00:02 UTC

Common default value of 2.

Description

Common default value of 2.

Usage

default(x)

Calculate the jth eba pvalue.

Description

Calculate the jth eba pvalue.

Usage

eba_pvalue(chisq, lambdas, j)

Get gamma from a model.

Description

Get gamma from a model.

Usage

gamma(m1, unbiased = 1, m0 = NULL)

Arguments

m1

Model to extract gamma from.

unbiased

Biased (1), unbiased (2), or both (3).

m0

Optional second model, used if m1 does not work.

Value

List of (un)biased gammas.

Calculate unbiased gamma from gamma and object.

Description

Calculate unbiased gamma from gamma and object.

Usage

gamma_to_gamma_unbiased(gammas, object)

Arguments

gammas

List of gammas for each group.

object

lavaan object that corresponds to gamma.

Value

List of unbiased gammas.

Calculate the scaled and shifted / the mean-variance adjusted p-value

Description

Calculate the scaled and shifted / the mean-variance adjusted p-value

Usage

scaled_and_shifted(chisq, lambdas)

Arguments

chisq

Chi-square fit value from a lavaan object.

lambdas

Eigenvalues of UG matrix.

Value

The scaled and shifted p-value or the mean-variance adjusted p-value.

Calculate nested ugamma.

Description

This can also be used with restrictions.

Usage

lav_ugamma_nested_2000(m0, m1, gamma, a = NULL, method = "delta")

Arguments

m0, m1

Two nested lavaan objects.

gamma

Gamma weighted by groups.

a

The A matrix. If if NULL, gets calculated by lavaan:::lav_test_diff_A with method = method.

method

Method passed to lavaan:::lav_test_diff_A.

Value

Ugamma for nested object.

Returns if not NA; else converts NA to NULL.

Description

Returns if not NA; else converts NA to NULL.

Usage

nanull(x)

Calculate the jth pall pvalue.

Description

Calculate the jth pall pvalue.

Usage

pall(chisq, lambdas)

Calculate the jth eba pvalue.

Description

Calculate the jth eba pvalue.

Usage

peba_pvalue(chisq, lambdas, j)

Calculate penalized OLS pvalue.

Description

Calculate penalized OLS pvalue.

Usage

pols_pvalue(chisq, lambdas, gamma)

Calculate the jth all pvalue.

Description

Calculate the jth all pvalue.

Usage

pvalue_all(chisq, lambdas)

P value function for one and two arguments.

Description

P value function for one and two arguments.

Usage

pvalues_(
  m0,
  m1,
  unbiased,
  trad,
  eba,
  peba,
  pols,
  chisq = c("ml", "rls"),
  extras = FALSE,
  method
)

Value

pvalues.

Calculate p-values for one or two lavaan objects.

Description

Calculate p-values for a lavaan object using several methods, including penalized eigenvalue block-averaging and penalized regression estimators. The recommended choices of p-values are included as default values. Multiple p-values can be returned simultaneously.

Usage

pvalues(object, tests = c("pEBA4_RLS"))

pvalues_nested(m0, m1, method = c("2000", "2001"), tests = c("PALL_UG_ML"))

Arguments

object, m0, m1

One or two lavaan objects. pvalues does goodness-of-fit testing on one object, pvalues_nested does hypothesis testing on two nested models.

tests

A list of tests to evaluate on the form "(test)_(ug?)_(rls?)"; see the default arguments and details below. The defaults are the recommended options.

method

For nested models, choose between 2000 and 2001. Note: 2001 and Satorra-Bentler will not correspond with the variant in the paper.

Details

The test argument is a list of character strings on the form (test)(ug?)(ml?), for instance, SB_UG_RLS.

The eba method partitions the eigenvalues into j equally sized sets (if not possible, the smallest set is incomplete), and takes the mean eigenvalue of these sets. Provide a list of integers j to partition with respect to. The method was proposed by Foldnes & Grønneberg (2018). eba with j=2 – j=4 appear to work best.

The peba method is a penalized variant of eba, described in (Foldnes, Moss, Grønneberg, 2024). It typically outperforms eba, and the best choice of j are typically about 2–6.

pols is a penalized regression method with a penalization term from ranging from 0 to infinity. Foldnes, Moss, Grønneberg (2024) studied pols=2, which has good performance in a variety of contexts.

pall uses all eigenvalues in ugamma, but penalizes them. This is the recommended option for nested models. all uses all eigenvalues.

In addition, you may specify a

The unbiased argument is TRUE if the the unbiased estimator of the fourth order moment matrix (Du, Bentler, 2022) is used. If FALSE, the standard biased matrix is used. There is no simple relationship between p-value performance and the choice of unbiased.

The chisq argument controls which basic test statistic is used. The ml choice uses the chi square based on the normal discrepancy function (Bollen, 2014). The rls choice uses the reweighted least squares statistic of Browne (1974).

Value

A named vector of p-values.

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

Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. https://psycnet.apa.org/record/1996-97111-016

Asparouhov, & Muthén. (2010). Simple second order chi-square correction. Mplus Technical Appendix. https://www.statmodel.com/download/WLSMV_new_chi21.pdf

Wu, H., & Lin, J. (2016). A Scaled F Distribution as an Approximation to the Distribution of Test Statistics in Covariance Structure Analysis. Structural Equation Modeling. https://doi.org/10.1080/10705511.2015.1057733

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

Bollen, K. A. (2014). Structural Equations with Latent Variables (Vol. 210). John Wiley & Sons. https://doi.org/10.1002/9781118619179

Browne. (1974). Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal. https://doi.org/10.10520/aja0038271x_175

Examples

library("semTests")
library("lavaan")
model <- "A =~ A1+A2+A3+A4+A5;
          C =~ C1+C2+C3+C4+C5"
n <- 200
object <- sem(model, psych::bfi[1:n, 1:10], estimator = "MLM")
pvalues(object)

# For the pEBA6 method with biased gamma and ML chisq statistic:
pvalues(object, "pEBA6_ML")

Calculate the scaled_f p-value.

Description

Calculate the scaled_f p-value.

Usage

scaled_f(chisq, eig)

Arguments

chisq

Chi-square fit value from a lavaan object.

eig

eig of UG matrix.

Value

scaled f p-value.

Create sparse matrix

Description

Create sparse matrix

Usage

sparsify(mat, lim = 1e-09)

Arguments

mat

Matrix input.

lim

Elements with absolute value less than lim get set to 0.

Value

Object of dgCMatrix.

Split string into options.

Description

Split string into options.

Usage

split_input(string)

Arguments

string

Input string

Calculate traditional pvalues.

Description

Calculate traditional pvalues.

Usage

trad_pvalue(
  df,
  chisq,
  lambdas,
  type = c("std", "sf", "ss", "sb", "pall", "all")
)

Arguments

df, chisq, lambdas, type

Parameters needed to calculate the p-values.

Value

Traditional p-values.

Calculate non-nested gamma

Description

Calculate non-nested gamma

Usage

ugamma(object, unbiased = 1)

Calculate nested gamma

Description

Calculate nested gamma

Usage

ugamma_nested(m0, m1, method = c("2000", "2001"), unbiased = 1)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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