Multiway Analysis of Multivariate Longitudinal Data
(Meerweganalyse van Multivariate Longitudinale Data)

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


Multivariate longitudinal analysis: Theory and practice

Researcher: Dr. F.J. Oort
Programmer: G.T. van Donselaar
Supervisor: Dr. P.M. Kroonenberg


[to be written]

Sequential multivariate analyse of qualitative variables based on transition tables

Researcher: Drs. M. de Rooij
Supervisor: Prof. dr. W.J. Heiser


Longitudinal categorical data are often represented in a transition table of which the dimensionality is equal to the number of time points considered. Such data are very common in social and behavioural sciences and are mostly analysed using loglinear analysis. A drawback of the method is the large number of parameters to be estimated and the interpretation of these parameters. The objective of this research project is to propose a multidimensional scaling method for such data that will alleviate these problems. The emphasis is on

Analysis of quantitative multivariate longitudinal data
using time-specific models

Researcher: Drs. M.E. Timmerman
Supervisors: Dr. H.A.L. Kiers and Prof. dr. J.M.F. ten Berge


Various techniques have been proposed for the analysis of quantitative multivariate longitudinal data. A number of those exploit the relation between data observed on successive time points, by explicitly taking such relations into account in the models used for representing such data. Examples of such techniques are longitudinal factor analysis, dynamic factor analysis, multivariate time series analysis, state space modelling and growth curve analysis. These techniques are all based on distributional assumptions that may not always be plausible in practice. when multivariate longitudinal data are observed on more than one observation unit, we actually deal with three-way data (observation units by variables by time points). Therefore, an alternative to the above mentioned techniques is furnished by techniques for exploratory three-way analysis, like parallel factor analysis and three-mode principal components analysis. These techniques do not employ distributional assumptions, and could hence be preferable in cases where such assumptions are violated. However, they also ignore the relations of scores at successive time points.

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.

Multivariate longitudinal analysis of qualitative variables without time-specific assumptions

Researcher: Drs. W.M.A. Weltens
Supervisors: Prof. dr. J.M.F. ten Berge and Dr. H.A.L. Kiers


It is useful to distinguish between two classes of methods for multivariate analysis of quantitative longitudinal data: Those that capitalise on the longitudinal or repeated measurement property of the data and those that ignore this type of information. In the former case, we speak of three-way methods, whereas methods of the latter type are referred to as cross-sectional methods: Each occasion of measurement is treated as if originating from a different set of individuals or objects.

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:

  1. The performance of the methods in recovering underlying structures under various noise conditions;
  2. The incremental performance of three-way methods over cross-sectional methods;
  3. The impact of standardising and other ways of preprocessing on the performance of the methods.
The main part of this research consists of the analysis of existing data and of simulated data.

Selected relevant publications of supervisors
(prior to the start of the project)

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