Assessment of maximum likelihood PCA missing data imputation. (8th June 2016) - Folch‐Fortuny, Abel; Arteaga, Francisco; Ferrer, Alberto
Abstract : Maximum likelihood principal component analysis (MLPCA) was originally proposed to incorporate measurement error variance information in principal component analysis (PCA) models. MLPCA can be used to fit PCA models in the presence of missing data, simply by assigning very large variances to the non‐measured values. An assessment of maximum likelihood missing data imputation is performed in this paper, analysing the algorithm of MLPCA and adapting several methods for PCA model building with missing data to its maximum likelihood version. In this way, known data regression (KDR), KDR with principal component regression (PCR), KDR with partial least squares regression (PLS) and trimmed scores regression (TSR) methods are implemented within the MLPCA method to work as different imputation steps. Six data sets are analysed using several percentages of missing data, comparing the performance of the original algorithm, and its adapted regression‐based methods, with other state‐of‐the‐art methods. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : The imputation step performed observation‐wise in the maximum likelihood principal component analysis (MLPCA) algorithm for missing data is equivalent to the imputation performed in the projection to the model plane method for principal component analysis model building. The MLPCA algorithm can be adapted to impute using regression‐based approaches, such as known data regression and trimmed score regression. Six datasets are used to compare the missing data imputations of MLPCA, the adapted MLPCA algorithm, and the original trimmed score regression and projection to the model plane methods.