inst/VALIDATION.md

In bifactory: (Bifactor) ESEM with Continuous (MLR) or Ordinal (WLSMV) Data

Validation summary (bifactory)

This note summarizes numerical checks against Mplus. Full reproduction scripts live in the package source repository under cran/validation/; that directory is not included in the CRAN tarball (see .Rbuildignore).

Continuous and ordinal single-group fits

| Dataset | N | Items | Factors | Checks | |---------|---|-------|---------|--------| | BAT3 | 495 | 23 | 4 (ESEM) | Loadings, SEs, CFI/TLI/RMSEA/SRMR (CFA, ESEM, B-ESEM; WLSMV and MLR) | | neil.csv | 197 | 18 | 3 | Same |

Scripts: validation/bat3_lavaan_vs_mplus.R, validation/neil_lavaan_vs_mplus.R.

Typical tolerances after lavaan 0.6-22.2568: loadings max |Δ| ≤ 0.001; SEs ≤ 0.008 (max across test set); fit indices to 3 decimal places.

Ordered B-ESEM

Default production path: besem_ordered(method = "rotation") (custom DWLS/WLSMV + orthogonal target rotation). Validated against Mplus ESTIMATOR = WLSMV; ROTATION = TARGET (orthogonal).

besem_ordered(method = "set-esem") is a restricted lavaan CFA and is not expected to match Mplus B-ESEM loadings.

Multi-group measurement invariance (lavaan path)

| Model | Data | Groups validated | Notes | |-------|------|------------------|-------| | B-ESEM ordinal | BFI (25 items, 5 specific + G) | G ∈ {2, 3, 4, 5} | df match Mplus at all six levels; max \|ΔCFI\| ≤ 0.001; max \|ΔSRMR\| ≤ 0.001; standardized loadings within 0.001 at all six levels and in every group once the R solution is carried into Mplus's rotation orientation (model-implied polychoric correlations within 0.001 as well); group-wise Procrustes alignment of standardized loadings understates the agreement in non-reference groups from the weak level on (0.01 to 0.02), because their free factor covariances make the standardization rotation-dependent | | B-ESEM ordinal | BAT 2023 (23 items, 4 specific + G) | G ∈ {2, 4, 8} | df match; see the paragraph below for what agrees and what does not | | ESEM ordinal | BFI | G ∈ {2, 3, 4} | Theta-parameterization identification fixes |

Caution: with many groups the R side is slow (bfi: 19 / 40 / 100 minutes at G = 3 / 4 / 5 on 25 items with the two starts of each level fitted one after the other; eight BAT countries about three and a half hours; the default cores = 2 fits the two starts at the same time with identical results, 13 instead of 18 minutes at G = 3), and the levels whose non-reference residual variances and factor covariances are empirically unidentified on your data (a non-positive-definite factor covariance matrix in some group) have no unique solution in any program---verify against external software before reporting them.

WLSMV χ² difference tests from lavTestLRT() may differ numerically from Mplus DIFFTEST. With identical df the WLSMV chi-square itself sits about 0.1 to 0.2 percent below Mplus's (2 to 4 units on bfi): both programs reach the same minimum of the fit function and use the same scaling and shift, but lavaan weights each group's discrepancy by n_g − 1 where Mplus uses n_g.

What agreement with Mplus requires (BAT 2023 check, 23 items, up to 8 countries, 0.6.0). lavaan ≥ 0.7-2 (earlier versions put sparse, highly correlated polychoric pairs up to 0.03 too high); Mplus run at a convergence criterion of 1e-6 or tighter (its default stopped 0.1 to 1 percent above its own optimum; the generated inputs now use 1e-6); and the configural fit started from the per-group optima, which esem_invariance() now does (the joint optimizer's path depends on the number of groups and left one country in a local optimum 9 percent above Mplus's; the starts are passed as a parameter table because lavaan caps a numeric start at 1000 entries and four bfi tiers or five BAT countries already need more). With those three in place, standardized loadings agree to about 0.01 after Procrustes alignment at every level whose fit function has one optimum. Two things stay apart and are properties of the data: levels with a non-positive-definite factor covariance matrix in some group (both programs report it, each settles in its own point), and from six groups on the latent-means model, which has two or three equally deep optima 0.11 to 0.16 apart; which one a program reaches depends on its starting values (at eight and at five groups lavaan's default start and Mplus's reach the same one, 0.011 and 0.006 apart, and esem_invariance() keeps the default start's solution unless a second start is deeper by more than 0.1 percent).

Reproducing checks locally

devtools::load_all("path/to/cran")
source("validation/bat3_lavaan_vs_mplus.R")  # requires Mplus output files

GitHub: https://github.com/leondebeer/bifactory

bifactory documentation built on Oct. 28, 2026, 1:06 a.m.