Idiographic Item Response Theory: Modeling Person-Specific Differential Item Functioning in Intensive Longitudinal Data

Idiographic theories of psychological measurement emphasize that the relationships between item responses and a latent trait may vary across individuals, yet typical item response theory (IRT) models assume item parameters are constant across persons. We propose an IRT approach for modeling person-specific (idiographic) heterogeneity in item functioning in intensive longitudinal data. We extend the two-parameter logistic IRT model to allow item location parameters to vary across individuals through person-by-item interaction random effects. We apply a Bayesian estimator to estimate item-specific interaction variances and use a regularizing spike-and-slab likelihood mixture to identify items with non-negligible heterogeneity. A simulation study indicates that the model recovers such heterogeneity reasonably well when person sample sizes and the number of repeated measurements are at least moderate. We then apply our approach to empirical data from a depression study and find substantial variation across items in the degree of person-specific item functioning. The proposed model and estimator contribute to emerging work on idiographic measurement by extending IRT to settings where repeated observations can be used to estimate individual departures from group-level item parameters, providing a new tool for studying differential item functioning, measurement invariance, and broader forms of individual variation in intensive longitudinal data.