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This paper concerns the construction of scaling models for large-scale assessments in education. A scaling model, which makes use of information from both responses to cognitive assessment and background survey items, produces plausible values for individual students. There are two major challenges when building a scaling model --  (1) a large number of background variables and (2) many missing values in the background survey data. To tackle these challenges, we propose a variable selection approach to latent regression modelling. The proposed approach handles missing data by iterative imputation and controls variable selection error by a data-splitting procedure.