Simple Imputation Methods versus Direct Likelihood Analysis for Missing Item Scores in Multilevel Educational Data

摘要

Missing data are ubiquitous in educational research settings, including item responses in multilevel data. Researchers in the Item Response Theory (IRT) context have shown that ignoring such missing data can create problems in the estimation of the IRT model parameters. Consequently, several imputation methods for dealing with missing item data have been proposed and shown to be effective when applied with traditional IRT models. Additionally, a non-imputation direct likelihood analysis has been shown to be an effective tool for handling missing observations in clustered data settings. This study investigates the performance of six simple imputation methods that have been found to be useful in other IRT contexts versus a direct likelihood analysis, in multilevel data from educational settings. Multilevel item response data were simulated based on two empirical datasets and part of the item scores were deleted such that they were either missing completely at random or missing at random. An explanatory IRT model was used for modeling the complete, incomplete and imputed datasets. It is shown that direct likelihood analysis of the incomplete datasets produces unbiased parameter estimates that are comparable to those of a complete data analysis. Multiple imputation approaches of the two-way means and corrected item means methods display varying degrees of effectiveness in imputing data that in turn can produce unbiased parameter estimates. The simple random imputation, adjusted random imputation, item means substitution and regression imputation methods seemed to be less effective in imputing missing item scores in multilevel data settings.Key words: Item Response Theory, multilevel data, missing data, imputation methods