Large scale assessment studies typically aim at investigating the relationship between persons competencies and explaining variables. Individual competencies are often estimated by explicitly including explaining background variables into corresponding Item Response Theory models. Since missing values in background variables inevitably occur, strategies to handle the uncertainty related to missing values in parameter estimation are required. We propose to adapt a Bayesian estimation strategy based on Markov Chain Monte Carlo techniques. Sampling from the posterior distribution of parameters is thereby enriched by sampling from the full conditional distribution of the missing values. We consider non-parametric as well as parametric approximations for the full conditional distributions of missing values, thus allowing for a flexible incorporation of metric as well as categorical background variables. We evaluate the validity of our approach with respect to statistical accuracy by a simulation study controlling the missing values generating mechanism. We show that the proposed Bayesian strategy allows for effective comparison of nested model specifications via gauging highest posterior density intervals of all involved model parameters. An illustration of the suggested approach uses data from the National Educational Panel Study on mathematical competencies of fifth grade students.