Many large-scale assessments model proficiency with a latent regression on contextual variables. Item-response data are used to estimate the parameters of the latent variable model and are used in conjunction with the contextual data to generate plausible values of individuals' proficiency attributes. These models typically incorporate numerous contextual variables to facilitate a broad scope of inferences, but ambitious increases in this scope introduces methodological challenges. Using analytical and simulation results, we isolate a source of estimation instability that imposes limits on this method, and explore this instability with respect to assessment designs, predictor selection, and other types of regression models. Based on the results, we provide suggestions to improve estimation in large-scale assessments.