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 817,100 replications organized into four phases:Phase 0: Adaptive MI Scoring Validation (3,600 replications)phase0_results.rds - Full replication-level results (MI severity × sample size × 200 reps)phase0_summary.rds - Aggregated summary statistics (sensitivity, specificity, AUC by condition)Phase 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 (9,900 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, increments of 0.05; 3,300 reps)phase2C_mi_trajectory.rds / .csv - MI severity trajectory (MI = 0.15–0.70, increments of 0.05; 3,600 reps)Phase 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 analysisFile 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