Toward Embedding-Based Psychometrics: Structural Modeling of Assessment-Item Semantics With Contextual Scores

arXiv:2609.31976v1 Announce Type: new Abstract: Contextual scores represent assessment items through their similarities to reference words in an external corpus. We examine the semantic structure of scores for 40 TIMSS mathematics scored units using a partially specified two-step factor procedure. A search across factor counts identifies a persistent seven-group structure under the featured construction. Subsequent comparisons consistently favor a general dimension alongside group associations, although individual group memberships remain sensitive to some specification choices. Item examples distinguish recurring, cross-domain, sensitive, and imposed associations. Simpler and unrestricted references clarify the contribution and limits of the anchored representation: it improves on a single factor but does not achieve the lowest working Bayesian information criterion (BIC). A separate response benchmark compares three initial Q constructions and their Hull-PVAF revisions under higher-order and saturated attribute distributions. Among these diagnostic models, BIC favors the official content framework and the Akaike information criterion (AIC) favors its direct four-factor augmentation, but a matched unidimensional two-parameter logistic model has lower AIC and BIC than all twelve conditions. These findings support a conditional semantic representation while limiting direct diagnostic interpretation. We discuss learned text-assisted response calibration as a prospective application requiring a larger calibrated item bank and independent evaluation.