Transitive differential item functioning clustering: A graph-theoretic approach to identifying many-group partial measurement invariance.

When measuring latent constructs across multiple demographic groups, identifying partial measurement invariance is essential for valid and fair comparisons. Recent advances, such as the neural network approach implemented in InterDIFNet, provide probabilistic differential item functioning (DIF) estimates for all pairwise group comparisons. However, InterDIFNet's output cannot be directly used for parameter estimation or ability scoring. To address this gap, we introduce transitive DIF clustering (TDC), a graph-theoretic algorithm that converts pairwise DIF probabilities into psychometrically coherent, measurement-invariant clusters that can be used to inform item parameter estimation and subsequent theta scoring. TDC represents groups as vertices and pairwise invariance as edges, and then enforces transitivity via a closure operation to identify logically consistent clusters. Extensive simulation studies show that TDC outperforms traditional clustering methods (K-means, hierarchical) and naive approaches (assuming full invariance or noninvariance), yielding more accurate and less biased latent score estimates. An empirical application illustrates TDC's ability to detect complex partial invariance patterns overlooked by conventional methods and its ability to inform initial item screening in operational assessments. By providing a reproducible, theoretically grounded approach to establishing partial measurement invariance across many groups, TDC advances the fair and valid assessment of latent constructs in educational and psychological research. (PsycInfo Database Record (c) 2026 APA, all rights reserved).