A new efficient method for determining the number of components in PARAFAC models

TLDR

The study proposes the core consistency diagnostic (CORCONDIA) to determine the proper number of components in multiway models, selecting the largest model that remains sufficiently appropriate. CORCONDIA evaluates the appropriateness of a PARAFAC (or restricted Tucker3) model by comparing fit improvements when incrementally adding component combinations, deeming a model appropriate if further additions do not significantly enhance fit. The diagnostic proved effective across diverse data sets for selecting component numbers in PARAFAC models, though simulations reveal that its theoretical foundations remain incomplete. © 2003 John Wiley & Sons, Ltd.

Abstract

Abstract A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the ‘appropriateness’ of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension‐wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete. Copyright © 2003 John Wiley & Sons, Ltd.