Factor Analysis of Multidimensional Polytomous Item Response Data Suffering From Ignorable Item Nonresponse

Abstract

This study deals with the problem of missing item responses in tests and questionnaires when factor analysis is used to study the structure of the items. Multidimensional rating scale data were simulated, and item scores were deleted under Rubin's (1976) MAR and MCAR definitions. Five imputation methods, the EM algorithm, and listwise deletion were implemented to deal with the item score missingness. Factor analysis was done on the complete data matrix, and on the seven data matrices that resulted from the application of each of the missingness methods. The factor loadings structure based on EM best approximated the loadings structure obtained from the complete data. Imputation of the mean per person across the available scores for that person was the best alternative to EM. It is recommended to researchers to use this simple method when EM is not available or when expertise to implement EM is lacking.