Multiple imputation for item scores when test data are factorially complex.

Multiple imputation under a two-way model with error is a simple and effective method that has been used to handle missing item scores in unidimensional test and questionnaire data. Extensions of this method to multidimensional data are proposed. A simulation study is used to investigate whether these extensions produce biased estimates of important statistics in multidimensional data, and to compare them with lower benchmark listwise deletion, two-way with error and multivariate normal imputation. The new methods produce smaller bias in several psychometrically interesting statistics than the existing methods of two-way with error and multivariate normal imputation. One of these new methods clearly is preferable for handling missing item scores in multidimensional test data.