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

Abstract

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.

Simple imputation methods versus direct likelihood analysis for missing item scores in multilevel educational data

“…Deterministic methods, however, assume that all conditions leading to missing item scores are perfectly known, an assertion that may not be entirely valid. Sijtsma and van der Ark (2003) discussed some simple methods and proposed two nonparametric single-imputation methods, one of which seemed to be superior in recovering several statistical properties of the original complete data from an incomplete data set. In addition, van Ginkel, van der Ark, and Sijtsma (2007) showed that multiple-imputation versions of some methods discussed by Sijtsma and van der Ark produced small discrepancies when compared to the statistical properties of the completely observed data.…”

Multiple Imputation of Missing Values Using the Response Function Method Based on a Data Set of the Health Assessment Questionnaire Disability Index

“…The RF imputation method was first proposed by Sijtsma and Van der Ark [2] for data related to test or scale. In the Rasch model, for a patient with a latent trait level, the probability of having a score x on item j is called the item response function, shown as, P(Xj=x|θ).…”

“…The RF imputation uses the estimated item response function to impute item scores, and it has been proven to be an efficient imputation method for unidimensional scales in simulation studies. [2][3][4] The classical test theory and item response theory…”

“…However, not every method is suitable for every missing data problem, so it is important to know the type of study being conducted before deciding on an appropriate method. The response function (RF) method was chosen for the imputation phase of the multiple imputation process [2] because of the nature of the data in this study and this approach's proven performance in recent simulation studies. [2][3][4] Nowadays, with the help of computer technology, imputation techniques of varying complexity have become available and are being employed in many disciplines, including the health sciences.…”

“…The response function (RF) method was chosen for the imputation phase of the multiple imputation process [2] because of the nature of the data in this study and this approach's proven performance in recent simulation studies. [2][3][4] Nowadays, with the help of computer technology, imputation techniques of varying complexity have become available and are being employed in many disciplines, including the health sciences. For example, rheumatology researchers have used imputation techniques to deal with the missing data problem in their studies [5,6] while others have investigated the missing data techniques themselves.…”