Abstract
The two most common component methods for the analysis of three-way data, CANDECOMP/PARAFAC (CP) and Tucker3 analysis, are used to summarize a three-mode three-way data set by means of a number of component matrices, and, in case of Tucker3, a core array. Until recently, no procedures for computing confidence intervals for the results from such analyses were available. Recently, such procedures have come available by Riu and Bro (2003) for CP using the jack-knife procedure, and by Kiers (2004) for CP and Tucker3 analysis using the bootstrap procedure. The present paper reviews the latter procedures, discusses their performance as reported by Kiers (2004), and illustrates them on an example data set.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
CARROLL, J.D. and CHANG, J-J. (1970): Analysis of individual differences in multidimensional scaling via an N way generalization of ”Eckart Young” decomposition. Psychometrika, 35, 283–319.
EFRON, B. and TIBSHIRANI, R.J. (1993): An introduction to the bootstrap. New York, Chapman & Hall.
GROENEN, P.J.F., COMMANDEUR, J.J.F. and MEULMAN, J.J. (1998): Distance analysis of large data sets of categorical variables using object weights. British Journal of Mathematical and Statistical Psychology, 51, 217–232.
HARSHMAN, R.A. (1970): Foundations of the PARAFAC procedure: models and conditions for an ”explanatory” multi-mode factor analysis. UCLA Working Papers in Phonetics, 16, 1–84.
KIERS, H.A.L. (1998): Joint orthomax rotation of the core and component matrices resulting from three-mode principal components analysis. Journal of Classification, 15, 245–263.
KIERS, H.A.L. (2004): Bootstrap confidence intervals for three-way methods. Journal of Chemometrics, 18, 22–36.
KIERS, H.A.L. and VAN MECHELEN, I. (2001): Three-way component analysis: Principles and illustrative application. Psychological Methods, 6, 84–110.
KROONENBERG, P.M. and DE LEEUW, J. (1980): Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika, 45, 69–97.
KRZANOWSKI, W.J. (1987): Cross-validation in principal component analysis. Biometrics, 43, 575–584.
MARKUS, M.T. (1994): Bootstrap confidence regions in nonlinear multivariate analysis. Leiden, DSWO Press.
MEULMAN, J.J. and HEISER, W.J. (1983): The display of bootstrap solutions in multidimensional scaling. Unpublished technical report, University of Leiden, The Netherlands.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Kiers, H.A. (2005). Bootstrap Confidence Intervals for Three-way Component Methods. In: Weihs, C., Gaul, W. (eds) Classification — the Ubiquitous Challenge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28084-7_7
Download citation
DOI: https://doi.org/10.1007/3-540-28084-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25677-9
Online ISBN: 978-3-540-28084-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)