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Three‐mode principal components analysis: Choosing the numbers of components and sensitivity to local optima
Author(s) -
Timmerman Marieke E.,
Kiers Henk A. L.
Publication year - 2000
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711000159132
Subject(s) - local optimum , principal component analysis , mode (computer interface) , mathematics , sensitivity (control systems) , mathematical optimization , computer science , statistics , electronic engineering , engineering , operating system
A method that indicates the numbers of components to use in fitting the three‐mode principal components analysis (3MPCA) model is proposed. This method, called DIFFIT, aims to find an optimal balance between the fit of solutions for the 3MPCA model and the numbers of components. The achievement of DIFFIT is compared with that of two other methods, both based on two‐way PCAs, by means of a simulation study. It was found that DIFFIT performed considerably better than the other methods in indicating the numbers of components. The 3MPCA model can be estimated by the TUCKALS3 algorithm, which is an alternating least squares algorithm. In a study of how sensitive TUCKALS3 is at hitting local optima, it was found that, if the numbers of components are specified correctly, TUCKALS3 never hits a local optimum. The occurrence of local optima increased as the difference between the numbers of underlying components and the numbers of components as estimated by TUCKALS3 increased. Rationally initiated TUCKALS3 runs hit local optima less often than randomly initiated runs.