Integration of latent space and confirmatory factor analysis to explain unexplained person-item interactions

As with many other latent variable models, the confirmatory factor analysis model is built upon the conditional independence assumption, which states that latent variables and item parameters can fully explain covariations between item responses. However, growing evidence in psychological and educational measurement research challenges this assumption, raising concerns regarding conditional dependence (CD). As the main model parameters correspond to the main person and item effects, CD implies the presence of unexplained person-item interactions. To leverage this information from nonbinary item responses, we propose integrating a latent space model with confirmatory factor analysis. The resulting model assumes that persons and items have co-ordinates on a shared metric space called an interaction map, where distances between persons and items reflect CD and their interactions. With this approach, the model quantifies and visualizes person-item interactions, leading to further practical analyses of CD. Our simulation studies demonstrate that the proposed model can recover its parameters well and correctly detect underlying CD. We also provide empirical examples to demonstrate the utilities and advantages of the proposed model, such as (a) deriving personalized diagnoses and evaluations for respondents, (b) quantifying individual differences in perceived item properties, and (c) facilitating investigations of CD with external variables and method effects. (PsycInfo Database Record (c) 2025 APA, all rights reserved).