Impact of Missing Data on Rasch Model Estimations

This study aims to investigate the effect of methods to deal with missing data on item difficulty estimations under different test length conditions and sampling sizes. In this line, a data set including 10, 20 and 40 items with 100 and 5000 sampling size was prepared. Deletion process was applied at the rates of 5%, 10% and 20% under conditions of completely missing at random (MCAR) and missing at random (MAR) data structures in these full data sets. Pursuant to deletion process, values were assigned through regression and mean imputation methods being among missing data methods. The method of leaving the missing data blank (non-imputation) was also examined. In Rasch model, CML, JML and Pairwise estimations of item difficulty parameter were evaluated in comparison with parameters estimated from full data sets. To this end, RMSE was used as an evaluation criterion. At the end of the research, the least amount of estimation errors was obtained in JML method of Rash model than CML and Pairwise methods and it was found that Pairwise method had similar performance as CML method. It was found that errors in the estimations obtained through three different estimation methods among the methods to deal with missing data increased as missing data rate increased, and decreased as sample size increased. In a big sampling, non-imputation of missing data and regression-based estimations offered good results under many conditions as missing data rate increased. It was found that test length affected CML and Pairwise estimations among missing data imputation methods under many conditions.