Influence of Imputation and EM Methods on Factor Analysis when Item Nonresponse in Questionnaire Data is Nonignorable

Abstract

This study deals with the influence of each of twelve imputation methods and two methods using the EM algorithm on the results of maximum likelihood factor analysis as compared with results obtained from the complete data factor analysis (no missing scores). Complete questionnaire rating scale data were simulated and, next, missing item scores were created under both ignorable and nonignorable nonresponse mechanisms. Next, imputation methods were used to fill the gaps and factor analysis was applied to both the original complete data and to the data sets including imputed scores. Each imputation method was implemented once with residual error and once without residual error. Also, one EM method estimated the factor loadings directly and the other estimated the complete data covariance matrix, which subsequently was factor analyzed. A design was analyzed with design factors Latent Trait Structure (technically called Mixing Configuration), Correlation Between Latent Traits, Nonresponse Mechanism, Percentage of Missingness, Sample Size, and Imputation Method. We found that, in general, methods that impute a score based on a respondent's mean score obtained from his/her observed item scores best recovered the factor loadings structure from the complete data. Moreover, for unidimensional data person mean methods with a residual error gave better results than the other imputation methods, either with or without a residual error component. For the EM methods a smaller design was analyzed. The conclusion was that both EM methods better recovered the complete data factor loadings than the imputation methods.