Handling Missing Data in Principal Component Analysis Using Multiple Imputation

Abstract

Principal component analysis (PCA) is a widely used tool for establishing the dimensional structure in questionnaire data. Whenever questionnaire data are incomplete, the missing data need to be treated prior to carrying out a PCA. Several methods exist for handling missing data prior to carrying out a PCA. The current chapter first discusses the most recent developments regarding the treatment of missing data in PCA. Next, of these methods, the method that is most promising both from a theoretical and practical point of view will be discussed in more detail, namely, multiple imputation. Finally, some extensions of multiple imputation to other PCA-related techniques or to statistics within PCA beyond the basics are discussed, and some general recommendations regarding the use of PCA on multiply imputed datasets in different statistical software packages will be given.

Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization

“…Missing values can be located in diGering patterns across a dataset, such as a small number of individual values across the data 11 , or a more structured pattern such as all measurements of a feature across many samples. A variety of imputation methods have been developed to predict missing values from existing measurements, each assuming diGerent existing relationships within the data [14][15][16] . For example, factorization-based imputation assumes the original data can be approximated by lower-rank matrices and seeks to fit the optimal factors from existing data 17,18 .…”