Weighted analysis for missing values in generalized procrustes analysis

Generalized Procrustes Analysis (GPA), a popular tool in sensory science, is generally carried out on panelist data matrices averaged over replicates. This paper addresses the problem of missing values arising when panelists miss sessions. Because this does not necessarily result in missing values in the final averaged data matrices, a weighted analysis is proposed with weights set proportional to the number of replicates for each panelist product combination. In a simulation study the weighted analysis gives a better match of the rotated panelist matrices (a lower loss) than the unweighted analysis although the resulting average configuration is not significantly closer to the true configuration. The weighted analysis is a straightforward extension to GPA for dealing with missing sessions and offers an improved basis on which to evaluate panelist performance.