Generating Multiple Imputations for Matrix Sampling Data Analyzed With Item Response Models

Sample survey designs in which each participant is administered a subset of the items contained in a complete survey instrument are becoming an increasingly popular method of reducing respondent burden ( Mislevy, Beaton, Kaplan, Sheehan 1992 ; Raghunathan & Grizzle, 1995 ; Wacholder, Carroll, Pee, Gail 1994 ). Data from these survey designs can be analyzed using multiple imputation methodology that generates several imputed values for the missing data and thus yields several complete data sets. These data sets are then analyzed using complete data estimators and their standard errors ( Rubin, 1987b ). Generating the imputed data sets, however, can be very difficult. We describe improvements to the methods currently used to generate the imputed data sets for item response models summarizing educational data collected by the National Assessment of Educational Progress (NAEP), an ongoing collection of samples of 4th, 8th, and 12th grade students in the United States. The improved approximations produce small to moderate changes in commonly reported estimates, with the larger changes associated with an increasing amount of missing data. The improved approximations produce larger standard errors.