Investigation and Treatment of Missing Item Scores in Test and Questionnaire Data

This article first discusses a statistical test for investigating whether or not the pattern of missing scores in a respondent-by-item data matrix is random. Since this is an asymptotic test, we investigate whether it is useful in small but realistic sample sizes. Then, we discuss two known simple imputation methods, person mean (PM) and two-way (TW) imputation, and we propose two new imputation methods, response-function (RF) and mean response-function (MRF) imputation. These methods are based on few assumptions about the data structure. An empirical data example with simulated missing item scores shows that the new method RF was superior to the methods PM, TW, and MRF in recovering from incomplete data several statistical properties of the original complete data. Methods TW and RF are useful both when item score missingness is ignorable and nonignorable.