Spatial Dependencies in Item Response Theory: Gaussian Process Priors for Geographic and Cognitive Measurement

Abstract: Measurement validity in Item Response Theory depends on appropriately modeling dependencies between items when these reflect meaningful theoretical structures rather than random measurement error. In ecological assessment, citizen scientists identifying species across geographic regions exhibit systematic spatial patterns in task difficulty due to environmental factors. Similarly, in Author Recognition Tests, literary knowledge organizes by genre, where familiarity with science fiction authors systematically predicts recognition of other science fiction authors. Current spatial Item Response Theory methods, represented by the 1PLUS, 2PLUS, and 3PLUS model family, address these dependencies but remain limited by (1) binary response restrictions, and (2) conditional autoregressive priors that impose rigid local correlation assumptions, preventing effective modeling of complex spatial relationships. Our proposed method, Spatial Gaussian Process Item Response Theory (SGP-IRT), addresses these limitations by replacing conditional autoregressive priors with flexible Gaussian process priors that adapt to complex dependency structures while maintaining principled uncertainty quantification. SGP-IRT accommodates polytomous responses and models spatial dependencies in both geographic and abstract cognitive spaces, where items cluster by theoretical constructs rather than physical proximity. Simulation studies demonstrate improved parameter recovery, particularly for item difficulty estimation. Empirical applications show enhanced recovery of meaningful difficulty surfaces and improved measurement precision across psychological, educational, and ecological research applications.