Package {semTests}

Type:	Package
Title:	Robust Test Statistics for Structural Equation Models
Description:	Computes robust p-values for overall fit and nested comparisons of structural equation models fitted with 'lavaan'. Implements penalized eigenvalue block averaging and penalized regression (Foldnes, Moss, Grønneberg, 2025) <doi:10.1080/10705511.2024.2372028>, including their extension to nested models (Foldnes, Grønneberg, Moss, 2026) <doi:10.3758/s13428-026-02968-4>, alongside familiar corrections such as Satorra-Bentler. Supported settings include complete-data ML, GLS, and ULS, categorical DWLS and ULS, and full-information maximum likelihood with one or several groups.
Version:	1.0.0
License:	GPL (≥ 3)
Encoding:	UTF-8
URL:	https://github.com/JonasMoss/semTests
Depends:	R (≥ 3.5.0)
Imports:	lavaan (≥ 0.7-2), methods
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
Config/testthat/edition:	3
Config/roxygen2/version:	8.0.0
NeedsCompilation:	no
Packaged:	2026-07-19 11:49:01 UTC; jonas
Author:	Jonas Moss [aut, cre], Njål Foldnes [ctb], Steffen Grønneberg [ctb]
Maintainer:	Jonas Moss <jonas.moss.statistics@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-19 15:40:02 UTC

Verify that two categorical fits define one comparable nested problem.

Description

Verify that two categorical fits define one comparable nested problem.

Usage

check_categorical_nested_pair(m0, m1)

Require a converged fit and flag inadmissible solutions.

Description

Require a converged fit and flag inadmissible solutions.

Usage

check_fit_quality(fit, arg = "object")

Reject anything that is not a fitted lavaan object.

Description

The class gate for pvalues() / pvalues_nested(). It must run before any @-slot access so a NULL / data.frame / list argument fails with a readable message instead of a cryptic S4 "no slot of name ..." error – the nested entry point in particular reads m0@test to compute the degrees of freedom before the support gate runs.

Usage

check_lavaan(x, arg = "object")

Arguments

Value

x, invisibly.

Verify that two fits describe one comparable nested problem.

Description

This gate checks fit-level compatibility that is required regardless of data type. It prevents a difference test across different samples, variables, groups, estimators, or information conventions. Substantive nesting still needs an argument based on the model specifications.

Usage

check_nested_pair(m0, m1)

Reject a fit whose configuration is outside the supported surface.

Description

The single entry-level gate for pvalues(). It admits exactly the configurations documented in semTests-support – the supported continuous and categorical estimators, complete data, and FIML with one or several groups – and stops with a pointer to ?semTests-support otherwise. Statistic- and gamma-specific rejections (the normal-theory-only RLS statistic and UG gamma) depend on the parsed test string and stay with the code that consumes them (make_chisqs() and gamma_matrices()). This gate checks the shape of the fit.

Usage

check_supported(fit, arg = "object")

Arguments

Value

fit, invisibly.

Reject a nested pair whose configuration is outside the supported surface.

Description

The single entry-level gate for pvalues_nested(): categorical nesting uses Satorra 2000 with a delta restriction map, missing-data nesting otherwise requires both fits to be FIML, and FIML nesting supports method = "2000" only. Each fit is also run through check_supported(). The UG-gamma rejection for FIML stays in the p-value engine because it depends on the parsed test string.

Usage

check_supported_nested(m0, m1, method, A.method = "delta")

Arguments

Value

TRUE, invisibly.

Compute p-values for one parsed test specification.

Description

Compute p-values for one parsed test specification.

Usage

compute_pvalues(
  m0,
  unbiased,
  trad,
  eba,
  peba,
  pols,
  chisq = c("ml", "rls"),
  m1 = NULL,
  A.method = "delta",
  fiml.convention = "observed"
)

Calculate the jth eba pvalue.

Description

Calculate the jth eba pvalue.

Usage

eba_pvalue(chisq, lambdas, j)

Align an H0 parameter basis to H1's full-parameter ordering.

Description

Align an H0 parameter basis to H1's full-parameter ordering.

Usage

fiml_align_parameter_basis(m0, m1, basis0)

Verify that two FIML fits use identical observations.

Description

Verify that two FIML fits use identical observations.

Usage

fiml_check_same_data(m0, m1)

Saturated observed-data FIML information in moment space.

Description

lavaan 0.7-2 exposes the corrected FIML H1 information. Setting h1.information on a local copy requests the unstructured, observed saturated information without refitting or changing the fitted parameters.

Usage

fiml_h1_information_observed(fit)

FIML goodness-of-fit eigenvalues.

Description

The observed convention uses observed saturated information, matching the convention independently implemented and validated in magmaan. The lavaan convention returns lavaan's own inspected UGamma spectrum.

Usage

fiml_lambdas(fit, df, fiml.convention = c("observed", "lavaan"))

FIML Satorra-2000 nested restriction eigenvalues.

Description

FIML Satorra-2000 nested restriction eigenvalues.

Usage

fiml_lambdas_nested(
  m0,
  m1,
  df,
  A.method = c("delta", "exact"),
  fiml.convention = c("observed", "lavaan")
)

Gamma-free nested FIML ingredients in H1's effective parameter space.

Description

Gamma-free nested FIML ingredients in H1's effective parameter space.

Usage

fiml_nested_ingredients(m1, fiml.convention = c("observed", "lavaan"))

Stable identities for lavaan's full free parameters.

Description

Stable identities for lavaan's full free parameters.

Usage

fiml_parameter_keys(fit)

Return the leading symmetric-product eigenvalues without forming AB.

Description

Return the leading symmetric-product eigenvalues without forming AB.

Usage

fiml_sandwich_eigenvalues(U, Gamma, df)

Extract model degrees of freedom through lavaan's public API.

Description

Extract model degrees of freedom through lavaan's public API.

Usage

fit_df(fit)

Provenance of a semTests_pvalues object.

Description

Records the fit-level options actually used to compute the p-values, so the returned object is self-describing across estimators and data types.

Usage

fit_provenance(
  fit,
  nested,
  method = NA,
  A.method = NA,
  fiml.convention = NA,
  df = NULL,
  tests = NULL,
  parsed_options = NULL
)

Get gamma from a model.

Description

Get gamma from a model.

Usage

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

Arguments

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

Value

List of unbiased gammas.

Upper tail of a linear combination of chi-square_1 variables

Description

Computes P(Q > q) for Q = \sum_j \lambda_j Z_j^2 with independent Z_j \sim N(0,1). Drop-in replacement for CompQuadForm::imhof(q, lambda)$Qq: the Imhof integral in the body of the distribution, a Lugannani-Rice saddlepoint in the far tail where the integral degrades.

Usage

imhof_pvalue(q, lambda)

Arguments

Value

Numeric vector of upper-tail probabilities, length length(q).

References

Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48(3/4), 419–426. doi:10.1093/biomet/48.3-4.419

Lugannani, R., & Rice, S. O. (1980). Saddle point approximation for the distribution of the sum of independent random variables. Advances in Applied Probability, 12(2), 475–490. doi:10.2307/1426607

Ruben, H. (1962). Probability content of regions under spherical normal distributions, IV: The distribution of homogeneous and non-homogeneous quadratic functions of normal variables. The Annals of Mathematical Statistics, 33(2), 542–570. doi:10.1214/aoms/1177704580

Is this the classical normal-theory, complete-data, random-x ML case?

Description

The Du-Bentler unbiased gamma and the RLS (browne.residual.nt.model) statistic are defined here. Other families use the biased gamma and the estimator's own uncorrected statistic.

Usage

is_classic_nt(fit)

Is this a continuous FIML/missing-data lavaan fit?

Description

Is this a continuous FIML/missing-data lavaan fit?

Usage

is_fiml(fit)

Reference spectrum of the nested test, without forming the full UGamma.

Description

For Satorra's (2000) method the nonzero eigenvalues are those of the ⁠m x m⁠ matrix ⁠C^{-1} D' Gamma D⁠ (see nested_factor_2000). This avoids the ⁠q x q⁠ UGamma and its eigendecomposition.

Usage

lambdas_nested(m0, m1, unbiased = 1, df)

Arguments

Value

A list of eigenvalue vectors, one per gamma estimate.

Calculate nested ugamma.

Description

This can also be used with restrictions.

Usage

lav_ugamma_nested_2000(m0, m1, gamma_matrix, a = NULL)

Arguments

Value

Ugamma for nested object.

Biased single-model spectrum exposed by lavaan.

Description

Biased single-model spectrum exposed by lavaan.

Usage

lavaan_lambdas(object, df)

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

Value

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

Stack lavaan's per-group moment derivatives.

Description

Stack lavaan's per-group moment derivatives.

Usage

model_delta_matrix(fit)

Moment derivatives with respect to effective model parameters.

Description

Moment derivatives with respect to effective model parameters.

Usage

model_effective_delta(fit)

Map effective model parameters to lavaan's full free-parameter space.

Description

Handles explicit equality-constraint bases, simple equality constraints, and equality constraints combined with inequalities or bounds.

Usage

model_parameter_basis(fit)

Gamma-free factors of the reduced nested spectrum (Satorra 2000).

Description

Returns the restriction-space factor D and companion C such that the m nonzero eigenvalues of the full ⁠q x q⁠ UGamma equal those of ⁠C^{-1} D' Gamma D⁠, an ⁠m x m⁠ problem with m the number of restrictions. This is the materialised reduction of Moss (2026): the full ⁠q x q⁠ U matrix and its eigendecomposition are never formed. With ⁠U = D C^+ D'⁠ one has ⁠D = V Delta P^+ A'⁠ and ⁠C = A P^+ A'⁠, where V is the (group-weighted) weight, Delta the Jacobian, ⁠P^+⁠ the inverted information, and A the restriction matrix.

Usage

nested_factor_2000(m0, m1, a = NULL)

Calculate the jth pall pvalue.

Description

Calculate the jth pall pvalue.

Usage

pall(chisq, lambdas)

Parse and validate public test specifications.

Description

Parse and validate public test specifications.

Usage

parse_tests(tests)

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)

Print method for p-values from pvalues() / pvalues_nested().

Description

Prints the p-values, then a one-line provenance footer (estimator, data type, information, df) recording the options used.

Usage

## S3 method for class 'semTests_pvalues'
print(x, ...)

Arguments

Value

x, invisibly.

Calculate the jth all pvalue.

Description

Calculate the jth all pvalue.

Usage

pvalue_all(chisq, lambdas)

Compute robust p-values for one or two lavaan objects

Description

Compute one or several p-values for a fitted lavaan model. Available methods include penalized eigenvalue block averaging, penalized regression, and familiar robust corrections. The defaults select the recommended method for the fitted model.

Usage

pvalues(
  object,
  tests = if (is_classic_nt(object)) "pEBA4_RLS" else "pEBA4",
  fiml.convention = c("observed", "lavaan")
)

pvalues_nested(
  m0,
  m1,
  method = c("2000", "2001"),
  tests = if (is_classic_nt(m0)) "PALL_UG_ML" else "PALL",
  A.method = c("delta", "exact"),
  fiml.convention = c("observed", "lavaan")
)

Arguments

Details

The tests argument is a character vector. Each element has one of the forms TEST, TEST_UG, TEST_ML, TEST_RLS, TEST_UG_ML, or TEST_UG_RLS. For example, SB_UG_RLS.

• The first part names the test. The available names are listed below.

• Add UG to use the unbiased estimator of the fourth-order moment matrix from Du and Bentler (2022). Leave it out to use the standard biased matrix. Performance depends on the data-generating process, so neither gamma choice dominates in every setting.

• The final part chooses the chi-square statistic. ML uses the normal-discrepancy statistic (Bollen, 1989). RLS uses Browne's (1974) reweighted least squares statistic.

The peba method is the recommended default. It partitions the eigenvalues into j equally sized sets (if not possible, the smallest set is incomplete), shrinks them towards their common mean, and averages within each set. Provide a positive integer j no greater than the test df. Values from 2 through 6 are usually good candidates. The method was introduced by Foldnes, Moss, and Grønneberg (2025).

pols is a penalized regression method with a finite positive penalization term. Foldnes, Moss, and Grønneberg (2025) studied pols=2, which has good performance in a variety of contexts.

pall penalizes all eigenvalues in ugamma, while all uses all eigenvalues without penalization. pall is the recommended option for nested models, for which the penalized methods were extended and evaluated by Foldnes, Grønneberg, and Moss (2026).

The eba method is the unpenalized predecessor of peba (Foldnes and Grønneberg, 2018). It averages within the eigenvalue blocks without shrinkage. peba usually performs better. eba remains available for comparisons, and values from j=2 through j=4 tend to work best.

Familiar corrections are available too:

• std uses the ordinary chi-square reference distribution.

• sb gives the Satorra–Bentler p-value (Satorra and Bentler, 1994).

• ss gives the scaled and shifted p-value (Asparouhov and Muthén, 2010).

• sf gives the scaled F p-value (Wu and Lin, 2016).

Estimators and data types

semTests-support (?semTests-support) gives the complete matrix of supported estimators, data types, and configurations. Here is the short version.

The limiting null law of the test statistic is a weighted sum of chi-squares for any minimum-discrepancy estimator. pvalues() supports ML/MLM/MLR, GLS, ULS, FIML (missing data), and categorical DWLS/ULS families, with single- and multi-group continuous, ordered, and mixed-indicator fits. pvalues_nested() supports continuous estimators and categorical Satorra-2000 comparisons with a delta restriction map. The fitted model must expose the asymptotic moment covariance. Robust choices such as test = "satorra.bentler" or estimator = "MLM", "MLR", or "DWLS" provide it. The RLS statistic (browne.residual.nt.model) and the unbiased (UG) Du-Bentler gamma are defined for the classical continuous, complete-data, random-x ML case. Other families use the standard statistic and biased gamma. Fixed or conditional observed exogenous predictors are currently refused. Full WLS/ADF is refused outright: its weight is already the inverse moment covariance, so the correction is exactly the identity and every test would equal the ordinary chi-square.

GLS, ULS, categorical DWLS/ULS, FIML missing data, and nested FIML or categorical comparison are validated to numerical tolerance against an independent implementation and are marked stable; see the Stability section in semTests-support.

Both entry points require a converged fit and warn if lavaan reports an inadmissible solution. Nested comparisons require the same requested estimator, fitting conventions, variables, groups, sample sizes, raw data, and missingness mask. semTests checks comparability. The substantive nesting argument remains part of the analysis.

For FIML, fiml.convention = "observed" (the default) uses observed saturated and model information throughout. An independent implementation validates this construction. The "lavaan" option reproduces lavaan 0.7-2's robust-test construction. For a single model it uses lavaan's inspected UGamma. For nested models it uses lavaan's H1 weight convention and selected model information. The returned object records the convention, which keeps this inferential choice visible in saved results.

For a single FIML model, "lavaan" means the eigenvalue spectrum returned by lavInspect(fit, "UGamma"). The scalar Yuan–Bentler–Mplus test stored by a default MLR fit is a different correction and may give a different result. For nested FIML models, "lavaan" reproduces lavTestLRT(..., method = "satorra.2000").

Value

A named numeric vector of p-values, of class semTests_pvalues, carrying an "semtests" attribute that records the requested tests, requested and base estimator, base-statistic and gamma choices, information type, data type, parameterization where applicable, nested method and restriction map where applicable, and degrees of freedom.

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. doi: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, 58, article 107. doi:10.3758/s13428-026-02968-4

Satorra, A. (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In R. D. H. Heijmans, D. S. G. Pollock, & A. Satorra (Eds.), Innovations in Multivariate Statistical Analysis (pp. 233–247). Kluwer Academic. doi:10.1007/978-1-4615-4603-0_17

Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507–514. doi:10.1007/BF02296192

Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent Variables Analysis: Applications for Developmental Research (pp. 399–419). Sage.

Asparouhov, T., & Muthén, B. O. (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. doi:10.1080/10705511.2015.1057733

Foldnes, N., & Grønneberg, S. (2018). Approximating Test Statistics Using Eigenvalue Block Averaging. Structural Equation Modeling, 25(1), 101–114. doi: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. doi:10.1080/10705511.2022.2063870

Kenward, M. G., & Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science, 13(3), 236–247. doi:10.1214/ss/1028905886

Bollen, K. A. (1989). Structural Equations with Latent Variables. John Wiley & Sons. doi:10.1002/9781118619179

Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 8, 1–24.

See Also

semTests-support for the full list of supported configurations.

Examples

library("semTests")
library("lavaan")
model <- "visual  =~ x1 + x2 + x3
          textual =~ x4 + x5 + x6
          speed   =~ x7 + x8 + x9"
object <- cfa(model, HolzingerSwineford1939, estimator = "MLM")
pvalues(object)

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

# Nested model comparison (constrain the textual loadings to be equal):
constrained <- "visual  =~ x1 + x2 + x3
                textual =~ a*x4 + a*x5 + a*x6
                speed   =~ x7 + x8 + x9"
m1 <- cfa(model, HolzingerSwineford1939, estimator = "MLM")
m0 <- cfa(constrained, HolzingerSwineford1939, estimator = "MLM")
pvalues_nested(m0, m1)

Requested lavaan estimator, before shortcut normalization.

Description

Requested lavaan estimator, before shortcut normalization.

Usage

requested_estimator(fit)

Calculate the scaled_f p-value.

Description

Calculate the scaled_f p-value.

Usage

scaled_f(chisq, eig)

Arguments

Value

scaled f p-value.

Supported estimators, data types, and configurations

Description

Use this page to check what pvalues() and pvalues_nested() support. The eigenvalue-based p-values target a limiting null law that is a weighted sum of chi-squares. This result holds for any minimum-discrepancy estimator and therefore includes estimators beyond normal-theory ML. The tables below give the supported combinations. Configurations outside them are refused at the entry point (see check_supported()), and the test suite follows the same boundary.

Details

Single-model (pvalues())

Nested (pvalues_nested())

Stability

The classical normal-theory ML path (continuous, complete data) is the mature, paper-backed core. The other supported estimators – GLS, ULS, categorical DWLS/ULS fits, FIML missing-data fits, and their nested comparisons – are also marked stable: each is validated to numerical tolerance against an independent implementation (magmaan) across a simulation battery, in addition to the deterministic implementation tests every available row carries. The fiml.convention = "lavaan" option reproduces lavaan's own spectrum for compatibility rather than as an independently validated construction. Configurations outside the tables are refused at the entry point.

Observed exogenous covariates

Observed exogenous predictors are supported when they are modeled jointly with the other variables. In lavaan, request this random-x analysis with fixed.x = FALSE and conditional.x = FALSE. The independent validation suite covers continuous ML, GLS, ULS, FIML, and mixed categorical DWLS in this setting, for single models and nested comparisons.

Fixed or conditional observed exogenous predictors are currently refused. Their reference distribution conditions on the realized covariate design and needs a separate saturated-model projection. If a covariate is intended to be fixed, keep that scientific choice and do not silently change it to random merely to pass the software check.

Fit quality and nested comparability

Both entry points require converged lavaan fits and warn when lavaan's post-estimation check reports an inadmissible solution. Nested comparisons additionally require the same requested estimator, fitting conventions, observed variables, groups, sample sizes, raw data, and missingness mask. These checks establish comparability. The scientific argument that one model is genuinely nested within the other still belongs in the analysis.

The constrained model belongs in m0. If the models are supplied in reverse df order, semTests warns and swaps them. Only the Satorra-2000 reduction is available. method = "2001" has been withdrawn because it performs poorly.

Statistic and gamma options

Test names use one of TEST, TEST_UG, TEST_ML, TEST_RLS, TEST_UG_ML, or TEST_UG_RLS (e.g. "SB_UG_RLS"). See pvalues() for the test families. Two of the options are defined only for the classical case:

• The RLS statistic (browne.residual.nt.model, Browne 1974) and the UG (Du-Bentler) unbiased gamma are available only for classical normal-theory ML with continuous, complete data, estimator = "ML", fixed.x = FALSE, and conditional.x = FALSE. lavaan degrades RLS to ADF elsewhere, and the Du-Bentler correction has no derivation for the other families or a fixed covariate design. semTests refuses either request and points you to the standard statistic and biased gamma.

• Categorical and mixed-indicator fits use lavaan's biased inspected UGamma spectrum and unscaled estimator statistic directly. Supported estimator families are DWLS (including WLSMV/WLSM/WLSMVS) and ULS (including ULSMV). Nested comparison is restricted to method = "2000" and A.method = "delta".

• Pairwise categorical missingness means support for lavaan's pairwise sample-statistic and UGamma calculation. Pairwise deletion has its own missingness assumptions and does not provide FIML or generally MAR-valid inference.

• FIML (missing data) uses the biased gamma and the standard statistic only. UG and RLS are refused. FIML supports one or several groups with continuous data. Observed exogenous predictors are supported under joint random-x inference, using fixed.x = FALSE and conditional.x = FALSE. fiml.convention = "observed" (the default) uses observed saturated and model information, following the recommendation of Kenward and Molenberghs (1998), and is independently validated against magmaan. "lavaan" reproduces lavaan 0.7-2's inspected robust-test spectrum, including its expected H1 weight.

Why full WLS/ADF is refused

For full WLS (ADF), with continuous or categorical sample statistics, the fitting weight is already the inverse of the asymptotic moment covariance, so UGamma is a projector: its nonzero eigenvalues are all exactly one and the eigenvalue correction collapses to the identity. Every robust p-value would therefore equal the ordinary 1 - pchisq(chisq, df). Because the correction adds nothing, full WLS is refused at the entry point. Fit a DWLS/ULS family for a non-degenerate robust test, or read the standard chi-square directly.

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. doi: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, 58, article 107. doi:10.3758/s13428-026-02968-4

Kenward, M. G., & Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science, 13(3), 236–247. doi:10.1214/ss/1028905886

Satorra, A. (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In R. D. H. Heijmans, D. S. G. Pollock, & A. Satorra (Eds.), Innovations in Multivariate Statistical Analysis (pp. 233–247). Kluwer Academic. doi:10.1007/978-1-4615-4603-0_17

See Also

pvalues(), pvalues_nested()

Signal a typed semTests error.

Description

Signal a typed semTests error.

Usage

semtests_abort(message, subclass = "semTests_error")

Signal a typed semTests warning.

Description

Signal a typed semTests warning.

Usage

semtests_warn(message, subclass = "semTests_warning")

Split string into options.

Description

Split string into options.

Usage

split_input(string)

Arguments

Calculate traditional pvalues.

Description

Calculate traditional pvalues.

Usage

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

Arguments

Value

Traditional p-values.

Calculate non-nested gamma

Description

Calculate non-nested gamma

Usage

ugamma(object, unbiased = 1)

Extract a stable leading UGamma spectrum.

Description

The theoretical spectrum is real and non-negative. Small negative or imaginary components arise from the nonsymmetric numerical representation of a matrix that is similar to a symmetric positive-semidefinite product. Numerical negatives are truncated; materially negative values are rejected.

Usage

ugamma_eigenvalues(ugamma, df, context = "UGamma")

Full nested UGamma reference used to validate the reduced implementation.

Description

Full nested UGamma reference used to validate the reduced implementation.

Usage

ugamma_nested_reference(m0, m1, unbiased = 1)

Validate public test specifications.

Description

Validate public test specifications.

Usage

validate_tests(tests)

Arguments

Value

tests, invisibly.