## Multiway/multimode analysis (43)

*Chair: Patrick Groenen, Wednesday 22nd July, 9.55 - 11.15, Castlereagh Room, Fisher Building***.**

**Henk Kiers** and Jos M.F. ten Berge, *Heymans Institute,* *University of Groningen, Heymans Institute, The Netherlands*. Comparison of PCA followed by procrustes analysis with multiset and three-way component analysis. (118)

**Tom Wilderjans**, Eva Ceulemans and Iven Van Mechelen, *Department of Psychology*, *Katholieke Universiteit Leuven, Belgium*. Methods for a global analysis of coupled data blocks that are subject to heterogeneity in the amount of noise. (198) ♥

**Yoshio Takane** and Zhidong Zhang, *Department of Psychology,* *McGill University, Montreal, Canada*. Algorithms for DEDICOM: acceleration, deceleration, or neither? (052)

**Kwanghee Jung**, Yoshio Takane and Heungsun Hwang, *Department of Psychology, McGill University, Canada*. An acceleration method for ten Berge et al.'s algorithm for orthogonal INDSCAL. (012B) ♥

ABSTRACTS

**Comparison of PCA followed by procrustes analysis with multiset and three-way component analysis**. (118)

*Henk Kiers and Jos M.F. ten Berge*

When confronted with a number of data sets X1,...,X*p *referring to the same variables, but not necessarily the same observation units, an often asked question is to what extent the structural relations between the variables are the same across the data sets. To assess this, one approach is to analyze all data matrices separately (e.g. by Principal Component Analysis), and then compare the loadings from all these analyses. For this comparison often (Generalized) Procrustes Analysis is used. An alternative approach, however, is to analyze all data sets jointly. When the data sets refer to the same observation units, such a joint analysis can be done by three-way component analysis techniques (e.g., Candecomp/Parafac or Tucker3 analysis). When the data sets refer to different sets of observation units, various simultaneous component analysis techniques are indicated. Since all three types of methods aim at summarizing and comparing the information in multiple data sets, the question is which method is best for each of these purposes (summarizing and comparing information). A theoretical comparison will be given first. This will be supplemented with some empirical (simulation based) studies on comparison of some specific variants of the different classes of techniques mentioned.

**Methods for a global analysis of coupled data blocks that are subject to heterogeneity in the amount of noise**. (198)

*Tom Wilderjans, Eva Ceulemans and Iven Van Mechelen
*In many fields of research, problems often result in the collection of coupled data, which may consist of different

*N*-way

*N*-mode data blocks that have one or more modes in common. In psychology, for example, often different pieces of information are available about the same persons, like, for instance, cognitive performance and physiological measures, implying a set of two coupled two-way data matrices. To get an overall picture of the mechanisms that may underlie the data in each of the data blocks, a global model may be used in which each data block is represented by a multi-way model, with the parameters for each shared mode being the same in all the multi-way models in which that shared mode is included; these common parameters may be estimated based on the information in all data blocks simultaneously. In this presentation, a set of novel global models will be introduced to analyze two-way and three-way coupled data blocks. Furthermore, we will discuss how analyses on the basis of the proposed models can be adjusted in order to deal with coupled data blocks that are subject to different amounts of noise (i.e., noise heterogeneity). The performance will be evaluated by means of extensive simulation studies and by means of applications to empirical real life coupled data.

**Algorithms for DEDICOM: acceleration, deceleration, or neither?** (052)

*Yoshio Takane and Zhidong Zhang*

Takane's original algorithm for DEDICOM (DEcomposition into DIrectional COMponents) was proposed more than two decades ago. There have been a couple of significant developments since then: Kiers et al.'s modification to ensure monotonic convergence of the algorithm, and Jennrich's recommendation to use the modified algorithm only when Takane's original algorithm violates the monotonicity. In this paper, we argue that neither of these modifications is essential, drawing a close relationship between Takane's algorithm and the simultaneous power method for obtaining dominant eigenvalues and vectors of a symmetric matrix. By ignoring monotonicity, we can develop a much more efficient algorithm by simple modifications of Takane's original algorithm, as demonstrated in this paper. More specifically, we incorporate the minimum polynomial extrapolation (MPE) method to accelerate the convergence of Takane's algorithm, and show that it significantly cuts down the computation time.

**An acceleration method for ten Berge et al.'s algorithm for orthogonal INDSCAL (012B)**

*Kwanghee Jung, Yoshio Takane and Heungsun Hwang*

INDSCAL (INdividual Differences SCALing) is a useful technique for investigating both common and unique aspects of K similarity data matrices. The model postulates a common stimulus configuration in a low-dimensional Euclidean space, while representing differences among the K data matrices by differential weighting of dimensions by different data sources. Since Carroll and Chang proposed their algorithm for INDSCAL, several issues have been raised: non-symmetric solutions, negative saliency weights, and the degeneracy problem. Orthogonal INDSCAL (O-INDSCAL) that imposes orthogonality constraints on the matrix of stimulus configuration has been proposed to overcome some of these difficulties. Ten Berge, Knol, and Kiers, and Trendafilov proposed algorithms for O-INDSCAL. In this paper, an acceleration technique called minimal polynomial extrapolation (MPE) is incorporated in ten Berge et al.'s algorithm. Simulation studies are conducted to compare the performance of the three algorithms (ten Berge et al.'s original algorithm, the accelerated algorithm, and Trendafilov's). Possible extensions of the accelerated algorithm to similar situations are also suggested.