Multiple imputation and maximum likelihood principal component analysis of incomplete multivariate data from a study of the ageing of port

A multivariate data matrix containing a number of missing values was obtained from a study on the changes in colour and phenolic composition during the ageing of port. Two approaches were taken in the analysis of the data. The first involved the use of multiple imputation (MI) followed by principal components analysis (PCA). The second examined the use of maximum likelihood principal component analysis (MLPCA). The use of multiple imputation allows for missing value uncertainty to be incorporated into the analysis of the data. Initial estimates of missing values were firstly calculated using the Expectation Maximization algorithm (EM), followed by Data Augmentation (DA) in order to generate five imputed data matrices. Each complete data matrix was subsequently analysed by PCA, then averaging their principal component (PC) scores and loadings to give an estimation of errors. The first three PCs accounted for 93.3% of the explained variance. Changes to colour and monomeric anthocyanin composition were explained on PC1 (79.63% explained variance), phenolic composition and hue mainly on PC2 (8.61% explained variance) and phenolic composition and the formation of polymeric pigment on PC3 (5.04% explained variance). In MLPCA estimates of measurement uncertainty is incorporated in the decomposition step, with missing values being assigned large measurement uncertainties. PC scores on the first two PCs after multiple imputation and PCA (MI+PCA) were comparable to maximum likelihood scores on the first two PCs extracted by MLPCA.