Multiway Analysis of Multivariate Longitudinal Data |

(Meerweganalyse van Multivariate Longitudinale Data) |

**Coördinator:**

Dr. H.A.L.
Kiers

University of Groningen,
Department of Psychology, Grote Kruisstraat 2/1, 9712 TS
Groningen, The Netherlands.

E-mail:
h.a.l.kiers at rug.nl

- Overview
- Projects
- Multivariate longitudinal analysis: Theory and practice
- Sequential multivariate analyse of qualitative variables based on transition tables
- Analysis of quantitative multivariate longitudinal data, using time-specific models
- Multivariate longitudinal analysis of qualitative variables without time-specific assumptions

- Selected publications of supervisors

- How to translate the transition frequencies into distances in low-dimensional space;
- How to represent a transition from a to be to c in the case of three time-points; from a to b to c to d in the case of four time points, etc.
- How to handle multivariate data in this framework;
- When to use two-way, three-way, or
*n*-way multidimensional scaling.

using time-specific models

In the present project, variants of these techniques will be developed that do take into account such time-specific relations, while still not relying on distributional assumptions. The main purpose of the project is to compare the resulting techniques for thee-way analysis to the afore-mentioned techniques based on distributional assumptions. The comparison will be based both on empirical data sets and on simulated data sets. In the former comparison, the techniques will be compared in terms of criteria like empirical plausibility, parsimony, and stability of solutions. In the latter comparisons, properties of the data will be varied systematically, and it will be assessed to what extent the techniques will recover those properties.

The present research is intended as a comparative evaluation of a variety of three-way methods, notably TUCKALS3, PARAFAC1, Latent change analysis and difference analysis, and cross-sectional methods as TUCKALS2, INDSCAL, PARAFAC2, simultaneous components analysis, latent difference analysis, and certain invariant factor models, some of which are protected against retest effects.

The key issues of interest are:

- The performance of the methods in recovering underlying structures under various noise conditions;
- The incremental performance of three-way methods over cross-sectional methods;
- The impact of standardising and other ways of preprocessing on the performance of the methods.

(prior to the start of the project)

- Heiser, W.J. (1988).

Selecting a stimulus set with prescribed structure from empirical confusion frequencies. British Journal of Mathematical and Statistical Psychology, 41, 37-51. - Heiser, W.J. & Bennani, M. (1995).

Triadic distance models for triadic dissimilarity data. Submitted manuscript. - Heiser, W.J. & Kroonenberg, P.M. (1997).

Triadic algorithms for the PARAFAC model with constraints. Intern rapport, Sectie M&T, Vakgroep Psychologie Rijksuniversiteit Leiden. - Kiers, H.A.L. (1991).

Hierarchical relations among three-way methods. Psychometrika, 56, 449-470. - Kiers, H.A.L. & Ten Berge, J.M.F. (1989).

Alternating least squares algorithms for Simultaneous Components Analysis with equal component weight matrices for all populations. Psychometrika, 54, 467- 473. - Kiers, H.A.L., & Ten Berge, J.M.F. (1994).

Hierarchical relations between methods for simultaneous component analysis and a technique for rotation to a simultaneous structure. British Journal of Mathematical and Statistical Psychology, 47, 109-126. - Kroonenberg, P.M. (1983).

Three mode principal component analysis: Theory and applications. Leiden: DSWO press. - Kroonenberg, P.M. (1994).

The TUCKALS line: A suite of programs for three-way analysis. Computational Statistics and Data Analysis, 18, 73-96. - Kroonenberg, P.M., Lammers, C.J., & Stoop, I. (1985).

Three-mode principal component analysis of multivariate longitudinal organizational data. Sociological Methods & Research, 14, 99-136. - Molenaar, P.C.M. (1985).

A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181-202. - Ten Berge, J.M.F. & Kiers, H.A.L. (1989).

Convergence properties of an iterative procedure of ipsatizing and standardizing a data matrix, with applications to Parafac/Candecomp preprocessing. Psychometrika, 21, 231-235. - Zielman, B. & Heiser, W.J. (1993).

Analysis of asymmetry by a slide vector. Psychometrika, 58, 101-114.

| Top | Meerweganalyse van Multivariate Longitudinale Data (in Dutch) | Centre for Child & Family Studies | The Three-Mode Company |

Education and Child Studies, Leiden University

Wassenaarseweg 52, 2333 AK Leiden, The Netherlands

Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945 E-mail: kroonenb at fsw.leidenuniv.nl

First version (month/day/year): 04/26/1999;