pvalues {semTests}

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 choice peba=4 together with chisq = "rls" and ub is recommended. Multiple p-values can be returned simultaneously.

Usage

pvalues(
  object,
  trad = NULL,
  eba = NULL,
  peba = c(2, 4),
  pols = 2,
  unbiased = 1,
  chisq = c("rls", "trad"),
  extras = FALSE
)

Arguments

object

A lavaan object.

trad

List of traditional p-values to calculate. Not calculated if NULL.

eba

List of which eba p-values to calculate. Not calculated if NULL.

peba

List of which peba p-values to calculate. Not calculated if NULL.

pols

List of penalization parameters to use in the penalized OLS p-value. Not calculated if NULL.

unbiased

A number between 1 and 3. 1: Calculate using the biased gamma matrix (default). 2: Calculate using the unbiased gamma matrix. 3: Calculate using both gammas.

chisq

Which chi-square statistic to base the calculations on.

extras

Returns the estimated eigenvalues and basic test statistics if checked.

Details

The traditional methods include:

• pstd the standard p-value where the choice of chisq is approximated by a chi square distribution.

• psb Satorra-Bentler p-value. The p-value proposed by Satorra and Bentler (1994).

• pss The scaled and shifted p-value proposed by Asparouhov & Muthén (2010).

• pcf The Scaled F p-value proposed by Wu and Lin (2016).

• pfull p-value based on all eigenvalues of the asymptotic covariance matrix matrix.

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 or j=4 appear to work best.

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

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

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 trad 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

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