Randomisation test for the number of dimensions of the group average space in generalised Procrustes analysis
2002
Wu, W. | Guo, Q. | Jong, S. de | Massart, D.L.
When generalised Procrustes analysis (GPA) is applied to analyse sensory data, it is important to decide the dimensionality, i.e. the number of principal component factors in the final group average space. Normally, it is empirically estimated based on the scree plot of the total explained variance and interpretability of dimensions, and no statistical method is available so far. In this paper, a new randomisation test was developed to detect significant dimensions of group average space obtained by GPA. It was developed from ANOVA and the consensus test which was originally proposed by Wakeling et al. especially for validation of GPA results. The method was applied to one conventional, two free choice profile sensory data sets and three simulated data sets. The results showed that the proposed randomisation F-test is more effective than the scree plot method. Compared with the Wakeling consensus test of GPA, it not only validates the consensus of data, but also identifies the significant dimensions of group average space. It successfully found significant factors for the three sensory data sets, and also correctly detected that there was no consensus in the first two simulated data sets, and there were two significant factors in the third simulated data set.
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