Title: A generalized partial credit model for network dependent latent traits with an application on modeling students' ability
Authors: Massimiliano Russo - Harvard Medical School (United States) [presenting]
Abstract: Partial credit models are widely used in item response theory to obtain interpretable inference when analyzing polytomous data. They map responses to items into continuous constructs that summarize individual latent traits. A main assumption of these models is that the latent traits are independent across subjects. This is a reasonable assumption when the measured individuals have few or no interactions. However, in some cases individual relationships are likely to be important predictors of the latent traits. For example, when monitoring students performances it is likely that high-achieving/low-achieving students bond together. Consequently, friends are likely to share similar latent trait values. To characterize the inter-individual dependence of the latent traits, we propose a novel generalized partial credit model that accounts for network connectivity patterns. Specifically, we rely on a conditional auto regressive (CAR) model for the distribution of an individual latent trait conditional to the others. The strength of the network dependence on the latent traits is directly quantified by the parameters of the CAR model, and can be tested from the data with a spike-and-slab prior. We illustrate the performance of the proposed model in simulations and in a real data application evaluating students' ability conditionally on their Facebook friendship network.