Multidimensional Latent Space Item Response Models: A Note on the Relativity of Conditional Dependence

Abstract Conditional dependence (CD) reflects potential interactions between persons and items in measurement, offering valuable information for deriving personalized diagnoses, evaluations, and feedback. The recent integration of psychometric models with latent space provides an effective way to visualize and quantify person–item interactions unexplained by latent variables and item parameters. In such applications, it is important to recognize the relative nature of CD, as models with different structures and complexities (e.g., due to factor dimensionality and item parameters) produce varying systematic explanations of person and item effects, leading to differing residual variations in both quantitative and qualitative sense. To demonstrate this relativity, we extend the previously developed unidimensional Rasch-based latent space item response model by incorporating between-item multidimensionality and item discrimination parameters. The resulting model can be reduced to simpler models with appropriate constraints, allowing us to explore the relativity in CD by comparing them. Simulation studies demonstrate that (1) the most complex proposed model properly recovers its parameters, (2) it outperforms the traditional IRT models by accounting for CD, and (3) the models in comparison exhibit distinctive extents of CD. The study continues with empirical examples that further illustrate relative changes in the extent and configurations of CD with practical implications.