University of Groningen,
Department of Psychology, Grote Kruisstraat 2/1, 9712 TS
Groningen, The Netherlands.
h.a.l.kiers at rug.nl
Multivariate longitudinal analysis: Theory and practice
Researcher: Dr. F.J.
Programmer: G.T. van Donselaar
Supervisor: Dr. P.M.
[to be written]
Sequential multivariate analyse of qualitative variables
based on transition tables
Researcher: Drs. M.
Supervisor: Prof. dr. W.J.
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
- How to translate the transition frequencies into distances in
- 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
- How to handle multivariate data in this framework;
- When to use two-way, three-way, or n-way
Analysis of quantitative multivariate longitudinal data
Researcher: Drs. M.E.
using time-specific models
Supervisors: Dr. H.A.L.
Prof. dr. J.M.F.
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
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
Prof. dr. J.M.F.
ten Berge and
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:
The main part of this research consists of the analysis of existing data
and of simulated data.
- The performance of the methods in recovering underlying structures
under various noise conditions;
- The incremental performance of three-way methods over
- The impact of standardising and other ways of preprocessing on
the performance of the methods.
Selected relevant publications of supervisors
(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
- Heiser, W.J. & Kroonenberg, P.M. (1997).
Triadic algorithms for the PARAFAC model with constraints. Intern
rapport, Sectie M&T, Vakgroep Psychologie Rijksuniversiteit
- Kiers, H.A.L. (1991).
Hierarchical relations among three-way methods. Psychometrika, 56,
- 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,
- 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,
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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
kroonenb at fsw.leidenuniv.nl
First version (month/day/year): 04/26/1999;