xmu_robust_ML_fit: xmu_robust_ML_fit

In umx: Structural Equation Modeling and Twin Modeling in R

xmu_robust_ML_fit

Description

Computes Satorra-Bentler (1994) robust scaling corrections and Brosseau-Liard & Savalei (2012) robust fit indices (CFI, TLI, RMSEA) for Maximum Likelihood models with raw continuous complete or incomplete (FIML) data.

Usage

xmu_robust_ML_fit(model, refModels = NULL)

Arguments

model	An OpenMx::mxModel() fitted with ML.
refModels	Reference models (Independence and Saturated models) to calculate incremental fit indices.

Details

The robust scaling correction factor c is computed using the difference between the trace of the saturated model and the trace of the fitted model, scaled by the degrees of freedom:

c = \frac{\mathrm{tr}(J_{\mathrm{saturated}}^{-1} B_{\mathrm{saturated}}) - \mathrm{tr}(J_{\mathrm{model}}^{-1} B_{\mathrm{model}})}{d}

where J = H/2 is the observed information matrix (reconciled from the Hessian H of -2\ln L) and B = G^T G is the outer product of the individual log-likelihood row gradients. Because OpenMx optimizes -2\ln L and G contains the row gradients of -2\ln L_i (which is 2 times the score s_i), the matrix product (H/2)^{-1} B scales to 4 J^{-1} K. Thus, dividing by 4 \times d scales the difference of these traces back to the Satorra-Bentler / Yuan-Bentler expectation scale.

Robust RMSEA is computed using Equation (5) of Brosseau-Liard, Savalei, and Li (2012):

\mathrm{RMSEA}_{\mathrm{robust}} = \sqrt{\max\left(0, \frac{\chi^2_{\mathrm{raw}} / N}{df} - \frac{c_{\mathrm{model}}}{N}\right)}

Value

A list containing scaling factors and adjusted robust fit statistics, or NULL if robust adjustments are not supported.

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_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_savalei_scaling_factor(), 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.