Direct Likelihood Analysis and Multiple Imputation for Missing Item Scores in Multilevel Cross-Classification Educational Data

Abstract

Multiple imputation (MI) has become a highly useful technique for handling missing values in many settings. In this article, the authors compare the performance of a MI model based on empirical Bayes techniques to a direct maximum likelihood analysis approach that is known to be robust in the presence of missing observations. Specifically, they focus on handling of missing item scores in multilevel cross-classification item response data structures that may require more complex imputation techniques, and for situations where an imputation model can be more general than the analysis model. Through a simulation study and an empirical example, the authors show that MI is more effective in estimating missing item scores and produces unbiased parameter estimates of explanatory item response theory models formulated as cross-classified mixed models.