Large-scale assessments (LSAs) use Mislevy's "plausible value" (PV) approach to relate student proficiency to noncognitive variables administered in a background questionnaire. This method requires background variables to be completely observed, a requirement that is seldom fulfilled. In this article, we evaluate and compare the properties of methods used in current practice for dealing with missing data in background variables in educational LSAs, which rely on the missing indicator method (MIM), with other methods based on multiple imputation. In this context, we present a fully conditional specification (FCS) approach that allows for a joint treatment of PVs and missing data. Using theoretical arguments and two simulation studies, we illustrate under what conditions the MIM provides biased or unbiased estimates of population parameters and provide evidence that methods such as FCS can provide an effective alternative to the MIM. We discuss the strengths and weaknesses of the approaches and outline potential consequences for operational practice in educational LSAs. An illustration is provided using data from the PISA 2015 study.