Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits
