Two-way imputation: A Bayesian method for estimating missing scores in tests and questionnaires, and an accurate approximation

Previous research has shown that method two-way with error for multiple imputation in test and questionnaire data produces small bias in statistical analyses. This method is based on a two-way ANOVA model of persons by items but it is improper from a Bayesian point of view. Proper two-way imputations are generated using data augmentation. Simulation results show that the resulting method two-way with data augmentation produces unbiased results in Cronbach's alpha, the mean of squares in ANOVA, the item means, and small bias in the mean test score and the factor loadings from principal components analysis. The data with imputed scores result in statistics having a slightly larger standard deviation than the original complete data. Method two-way with error produces results that are only slightly more biased, especially for low percentages of missingness. Thus, it may serve as an accurate approximation to the more involved method two-way with data augmentation.