Core consistency diagnostic in PARAFAC2

PARAFAC2 is applied in multiple research areas, for example, where data containing shifts are analysed, but it is a challenge to determine the appropriate number of components in the model. In this paper, it is hypothesized that the core consistency diagnostic, which is currently applied in, for example, PARAFAC1 can be used to determine model complexity in PARAFAC2. Theoretically, a PARAFAC1 model is fitted inside' the PARAFAC2 algorithm, and it should therefore be possible to apply the core consistency diagnostic from PARAFAC1 in PARAFAC2. To support this hypothesis, three different datasets, as well as simulated datasets, have been evaluated by means of PARAFAC2, and the core consistencies have been investigated. There is a general trend that if the core consistency is low, the model is overfitted as in PARAFAC1. Also, core consistency captures the true variation in the data, whereas small peaks are easily overlooked by visual inspection of noisy models. However, for determining the number of components in a PARAFAC2 model, we suggest usage of the core consistency in combination with other model parameters such as residuals, loadings, and split-half analysis. Copyright (c) 2013 John Wiley & Sons, Ltd.