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:<b>Phase 0: Adaptive MI Scoring Validation (3,600 replications)</b><code>phase0_results.rds</code> / <code>.csv</code> — Full replication-level results (MI severity × sample size × 200 reps)<code>phase0_summary.rds</code> — Aggregated summary statistics (sensitivity, specificity, AUC by condition)<b>Phase 0 Ablation: Weight Sensitivity Analysis (3,600 replications, same data)</b><code>phase0_ablation_results.rds</code> / <code>.csv</code> — Five weighting variants (Full, DP only, RP×DP, VS×DP, Equal) with AUC and Cohen's d<code>phase0_ablation_summary.rds</code> — Aggregated AUC and d by MI severity and sample size<code>phase0_ablation_auc.csv</code> / <code>phase0_ablation_d.csv</code> — Condition-level summaries<b>Phase 1: Core Performance Evaluation (800,000 replications)</b><code>phase1_results_full.rds</code> / <code>.csv</code> — Complete simulation results<code>Phase1_By_K.csv</code> — Results aggregated by number of groups (K = 5, 6, 7, 8, 9, 10, 15, 20)<code>Phase1_By_n.csv</code> — Results aggregated by sample size (n = 50, 100, 200, 500, 1000)<code>Phase1_By_MI.csv</code> — Results aggregated by MI severity (0.20, 0.30, 0.45, 0.65)<code>Phase1_Overall_Summary.csv</code> — Summary statistics across all conditions<code>Phase1_TypeI_Error.csv</code> — Type I error rates for Null and Moderator scenarios<b>Phase 2: Sensitivity Analyses (117,900 replications)</b><code>phase2A_bootstrap_convergence.rds</code> / <code>.csv</code> — Bootstrap iteration convergence (B = 500, 1000, 2000; 3,000 reps)<code>Phase2A_Convergence.csv</code> / <code>Phase2A_Stability.csv</code> — Convergence summary statistics<code>phase2B_noise_trajectory.rds</code> / <code>.csv</code> — Noise robustness (σ_ε = 0.20–0.70; 3,300 reps)<code>phase2C_mi_trajectory.rds</code> / <code>.csv</code> — MI severity trajectory (MI = 0.15–0.70; 3,600 reps)<code>phase2d_near_moderator_results.rds</code> / <code>.csv</code> — Near-moderator robustness (β_{ξ×Z} = 0.00–0.25, K × n × MI full factorial; 108,000 reps)<code>phase2d_summary.rds</code> / <code>.csv</code> — Aggregated FPR by interaction strength<b>Phase 3: Boundary Condition Testing (3,600 replications)</b><code>phase3_boundary_conditions.rds</code> / <code>.csv</code> — Complete boundary results<code>Phase3_By_Config.csv</code> — Results by configuration (18 extreme conditions)<code>Phase3_By_Dimension.csv</code> — Results aggregated by dimension tested<code>Phase3_Extreme_Cases.csv</code> — Worst-case scenario analysis<b>Phase 4: CFA-Based SVT Validation (24,000 replications)</b><code>phase4_cfa_results.rds</code> / <code>.csv</code> — Full factorial results (3 scenarios × 4 K × 5 n × 4 MI × 100 reps)<code>phase4_cfa_summary.rds</code> — Aggregated power and effect sizes by K and MI<b>File Formats:</b><code>.rds</code> files: Compressed R-native format (recommended for R users)<code>.csv</code> 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