Exploring the Comparability of Measurements – Empirical Benchmarks and Detectability Thresholds for Configural Invariance with EGA Trees

Exploratory Graph Analysis (EGA) trees detects configural non-invariance without a priori group specifications, yet interpreting the Network Difference (ND) index remains challenging due to a lack of empirical benchmarks. To address this, we conducted a large-scale Monte Carlo simulation (18,500 repetitions) using the ADEMP framework to evaluate detection sensitivity. By manipulating violation types, intensity (δ), number of affected items, and sample size (N), we modeled detection probability as a function of ND and N. Results revealed a conservative empirical Type I error rate (.008). Crucially, we derived sample-size-specific critical thresholds (τND) for 80% statistical power, demonstrating that required ND significantly decreases as sample size increases. We identify N = 400 (τND = .517) as the minimum functional baseline for detecting common configural non-invariance. To support research design and measurement validation, we complement these benchmarks with annotated R code and step-by-step tutorials, providing a ready-to-use resource for empirical and instructional applications.