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Some new methods for three-mode factor analysis and multi-set factor analysis

PhD ceremony:Ms T.T.T. (Tam) Lam
When:February 19, 2015
Supervisor:prof. dr. R.R. (Rob) Meijer
Co-supervisor:Prof. A.W. Stegeman
Where:Academy building RUG
Faculty:Behavioural and Social Sciences
Some new methods for three-mode factor analysis and multi-set
factor analysis

In this thesis, we focus on Exploratory Component Analysis and Common Factor Analysis techniques for multi-way and multi-set data.  Exploratory Component Analysis of a 4-way dataset of Belief in a Just World (BJW) data is discussed. The subjects are asked how strongly they believe that a number of 6 actors  (Natural,  God,  Human Institutions, Other People, Yourself, and Chance) bring about justice in the world for themselves or other people.  Our analysis includes exploring the correlation structure and conducting a PCA of two-way unfoldings of (part of) the dataset.  Also,  we fit Tucker3 to three-way parts of the dataset,  and Tucker4 to the complete dataset.  We also discuss how to rotate a Tucker4 rotation to simple structure.

For the topic of Common Factor Analysis,  we  propose and demonstrate new methods of three-mode  and multi-set factor analysis that make use of Minimum Rank Factor Analysis (MRFA), and Candecomp/Parafac or Tucker3 (for three-mode factor analysis),  and Parafac2 (for multi-set factor analysis). Using these methods, one can compute the overall percentage of explained common variance,  and also for each variable separately. This is usually not possible for existing methods of three-mode or multi-set factor analysis. Moreover, the algorithms that we propose are simple and easy to run. Our solutions are easy to interpret and our models are parsimonious. Finally, we classify the three-mode and multi-set component and factor models featured in the thesis in a 2x2x3 array of models. We briefly discuss how a suitable model can be chosen to analyze a three-mode or multi-set dataset.