Simulation Data for "Stabilizer Variables for Measurement Invariance–Induced Heterogeneity: Identification Theory and Testing in Multi-Group Models"

This dataset accompanies the manuscript "Stabilizer Variables for Measurement Invariance–Induced Heterogeneity: Identification Theory and Testing in Multi-Group Models".The study is a Monte Carlo simulation study and does not use empirical data. The repository contains simulation results from 949,100 replications organized into six phases:Phase 0: Adaptive MI Scoring Validation (3,600 replications)phase0_results.rds / .csv — Full replication-level results (MI severity × sample size × 200 reps)phase0_summary.rds — Aggregated summary statistics (sensitivity, specificity, AUC by condition)Phase 0 Ablation: Weight Sensitivity Analysis (3,600 replications, same data)phase0_ablation_results.rds / .csv — Five weighting variants (Full, DP only, RP×DP, VS×DP, Equal) with AUC and Cohen's dphase0_ablation_summary.rds — Aggregated AUC and d by MI severity and sample sizephase0_ablation_auc.csv / phase0_ablation_d.csv — Condition-level summariesPhase 1: Core Performance Evaluation (800,000 replications)phase1_results_full.rds / .csv — Complete simulation resultsPhase1_By_K.csv — Results aggregated by number of groups (K = 5, 6, 7, 8, 9, 10, 15, 20)Phase1_By_n.csv — Results aggregated by sample size (n = 50, 100, 200, 500, 1000)Phase1_By_MI.csv — Results aggregated by MI severity (0.20, 0.30, 0.45, 0.65)Phase1_Overall_Summary.csv — Summary statistics across all conditionsPhase1_TypeI_Error.csv — Type I error rates for Null and Moderator scenariosPhase 2: Sensitivity Analyses (117,900 replications)phase2A_bootstrap_convergence.rds / .csv — Bootstrap iteration convergence (B = 500, 1000, 2000; 3,000 reps)Phase2A_Convergence.csv / Phase2A_Stability.csv — Convergence summary statisticsphase2B_noise_trajectory.rds / .csv — Noise robustness (σ_ε = 0.20–0.70; 3,300 reps)phase2C_mi_trajectory.rds / .csv — MI severity trajectory (MI = 0.15–0.70; 3,600 reps)phase2d_near_moderator_results.rds / .csv — Near-moderator robustness (β_{ξ×Z} = 0.00–0.25, K × n × MI full factorial; 108,000 reps)phase2d_summary.rds / .csv — Aggregated FPR by interaction strengthPhase 3: Boundary Condition Testing (3,600 replications)phase3_boundary_conditions.rds / .csv — Complete boundary resultsPhase3_By_Config.csv — Results by configuration (18 extreme conditions)Phase3_By_Dimension.csv — Results aggregated by dimension testedPhase3_Extreme_Cases.csv — Worst-case scenario analysisPhase 4: CFA-Based SVT Validation (24,000 replications)phase4_cfa_results.rds / .csv — Full factorial results (3 scenarios × 4 K × 5 n × 4 MI × 100 reps)phase4_cfa_summary.rds — Aggregated power and effect sizes by K and MIFile Formats:.rds files: Compressed R-native format (recommended for R users).csv files: Human-readable format (compatible with Python, Excel, etc.)R code for reproducing all simulations is available at: https://github.com/sy142/stabilizer-variable-simulations