Combination Rules for Multiple Imputation in Three-Way Analysis Illustrated with Chromatography Data

In this paper we present a four-step procedure for performing a Tucker2 analysis on three-way data in the case a number of observations are missing. The procedure consists of (1) creating multiple complete data sets via multiple imputation of the missing data, (2) analysing these data sets with the Tucker2 model, (3) combining both the row and the column component matrices of these analyses to create centroid solutions using Generalised Procrustes analyses, and (4) using these centroid solutions to find the associated core slices appertaining to the centroid solutions. This procedure will produce both the basic parameters of the Tucker2 model and estimates of their variability due to the missing data. Chromatographic data are used as an illustration.