Factor Analysis and Missing Data

Abstract

The authors study the estimation of factor models and the imputation of missing data and propose an approach that provides direct estimates of factor weights without the replacement of missing data with imputed values. First, the approach is useful in applications of factor analysis in the presence of missing data. Second, the proposed factor analysis model may be used as a vehicle for imputing missing data, producing a complete data set that can be analyzed subsequently with some other method. Here, the factor model itself is not of primary interest but presents a suitable model for purposes of imputation. The proposed method accommodates various patterns of missing data commonly found in marketing. The framework for factor analysis the authors develop deals with both discrete and continuous variables and gives rise to several models not considered previously. The authors illustrate various factor models on synthetic data, investigating their performance when missing data are present and when the distribution of the observed variables is incorrectly specified. The authors provide two empirical studies of the performance of the approach. In the first, the authors demonstrate how the proposed approach recovers the true (complete-data) factor structure in the presence of missing observations that occur because of item nonresponse and compare the procedure with three alternative methods traditionally used for handling missing data in factor analysis. In the second application, the factor model is used as a vehicle to impute data that are missing by design.