xmu_savalei_scaling_factor: Savalei (2021) target scaling factor \hat{c}_3 for ordinal...

In umx: Structural Equation Modeling and Twin Modeling in R

Savalei (2021) target scaling factor \hat{c}_3 for ordinal WLS

Description

Computes the mean-and-variance correction used in robust CFI, TLI, and RMSEA for ordinal/categorical WLS models (Savalei, 2021; Brosseau-Liard & Savalei, 2012 noncentrality form).

Usage

xmu_savalei_scaling_factor(
  jacFull,
  jacPoly,
  vCatMlPoly,
  gammaPoly,
  wPolyWiU,
  wFullScaled,
  dfCatMl
)

Arguments

jacFull	Full aligned WLS Jacobian \Delta_{full} (all moments).
jacPoly	Polycorrelation rows \Delta_{poly}.
vCatMlPoly	catML V matrix (polycor block).
gammaPoly	Sample moment covariance \Gamma_{poly}.
wPolyWiU	WLS weight polycor block W_{poly} for the W_i U sandwich.
wFullScaled	Full aligned weight matrix at sample scale (n \times per-obs).
dfCatMl	Target model test degrees of freedom df_3.

Details

Formula. Let W_i U = I - \Delta_{poly} E^{-1} \Delta_{poly}' W_{poly}. Then

\hat{c}_3 = \frac{\mathrm{tr}\big( W_i U' \, V \, W_i U \, \Gamma_{poly} \big)}{df_3}

where:

• V = catML expected information (xmu_catml_wls_v())

• \Gamma_{poly} = sample moment covariance from OpenMx asymCov

• W_{poly} = WLS useWeight polycor block at sample scale

• E^{-1} = (\Delta_{full}' W_{full} \Delta_{full})^{-1} from the same fitted model and weight scaling

• df_3 = target model test df (not a polycor Jacobian rank shortcut)

Design note. V comes from the catML correlation scaffold; \Gamma and W come from the ordinal WLS fit. They are different statistical objects serving different roles in Savalei's correction. Do not substitute asymCov for V, or solve(useWeight) for \Gamma.

Value

Numeric \hat{c}_3, or NA_real_ if computation fails.

References

Savalei, V. (2021). Improving fit indices in SEM with categorical data. Multivariate Behavioral Research, 56(3), 390–407.

See Also

Other xmu internal not for end user: mx_make(), umxModel(), umxRenameMatrix(), umx_APA_pval(), umx_fun_mean_sd(), umx_get_bracket_addresses(), umx_make(), umx_standardize(), umx_string_to_algebra(), xmuHasSquareBrackets(), xmuLabel_MATRIX_Model(), xmuLabel_Matrix(), xmuLabel_RAM_Model(), xmuMI(), xmuMakeOneHeadedPathsFromPathList(), xmuMakeTwoHeadedPathsFromPathList(), xmuMaxLevels(), xmuMinLevels(), xmuPropagateLabels(), xmuRAM2Ordinal(), xmuTwinSuper_Continuous(), xmuTwinSuper_NoBinary(), xmuTwinUpgradeMeansToCovariateModel(), xmu_CI_merge(), xmu_CI_stash(), xmu_DF_to_mxData_TypeCov(), xmu_PadAndPruneForDefVars(), xmu_WLS_align_jacobian(), xmu_WLS_align_weight(), xmu_WLS_polycor_names(), xmu_ace_de_apply_censor_thresholds(), xmu_ace_de_parse_censor_meta(), xmu_ace_de_parse_censor_rule(), xmu_ace_de_release_binary_v1(), xmu_bracket_address2rclabel(), xmu_catml_df3_diagnostic(), xmu_catml_discrepancy_at_WLS(), xmu_catml_eval_model(), xmu_catml_implied_correlation(), xmu_catml_wls_v(), xmu_cell_is_on(), xmu_check_levels_identical(), xmu_check_needs_means(), xmu_check_variance(), xmu_clean_label(), xmu_compare_constraint_note(), xmu_compare_robust_ML(), xmu_data_missing(), xmu_data_swap_a_block(), xmu_describe_data_WLS(), xmu_dot_make_paths(), xmu_dot_make_residuals(), xmu_dot_maker(), xmu_dot_move_ranks(), xmu_dot_rank_str(), xmu_extract_column(), xmu_get_CI(), xmu_has_summary_mxData(), xmu_invert_matrix(), xmu_is_ordinal_WLS(), xmu_lavaan_process_group(), xmu_make_TwinSuperModel(), xmu_make_bin_cont_pair_data(), xmu_make_mxData(), xmu_match.arg(), xmu_mxData_summary(), xmu_mxRefModels(), xmu_name_from_lavaan_str(), xmu_path2twin(), xmu_path_regex(), xmu_print_algebras(), xmu_ram_de_apply_censor_thresholds(), xmu_ram_de_parse_censor_meta(), xmu_rclabel_2_bracket_address(), xmu_relevel_factors(), xmu_require_summary_mxData(), xmu_robust_ML_fit(), xmu_safe_run_summary(), xmu_savalei_fit_cfi(), xmu_savalei_fit_rmsea(), xmu_savalei_fit_tli(), xmu_savalei_null_scaling_factor(), xmu_savalei_polycor_blocks(), xmu_set_sep_from_suffix(), xmu_show_fit_or_comparison(), xmu_simplex_corner(), xmu_standardize_ACE(), xmu_standardize_ACEcov(), xmu_standardize_ACEv(), xmu_standardize_CP(), xmu_standardize_IP(), xmu_standardize_LISREL(), xmu_standardize_RAM(), xmu_standardize_SexLim(), xmu_standardize_Simplex(), xmu_start_value_list(), xmu_starts(), xmu_summary_RAM_group_parameters(), xmu_threshold_id_RAM(), xmu_threshold_id_twin_check(), xmu_topo_sort(), xmu_twin_add_WeightMatrices(), xmu_twin_check(), xmu_twin_get_var_names(), xmu_twin_make_def_means_mats_and_alg(), xmu_twin_upgrade_selDvs2SelVars(), xmu_update_covar(), xmu_wls_display_chi(), xmu_wls_extract_WV()

umx documentation built on Oct. 11, 2026, 5:07 p.m.