Abstract
Several techniques (like MDS and PCA) exist for summarizing data by means of a graphical configuration of points in a low-dimensional space. Usually, such analyses are applied to data for a sample drawn from a population. To assess how accurate the sample based plot is as a representation for the population, confidence intervals or ellipsoids can be constructed around each plotted point, using the bootstrap procedure. However, such a procedure ignores the dependence of variation of different points across bootstrap samples. To display how the variations of different points depend on each other, we propose to visualize bootstrap configurations in a bootstrap movie.
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
CLIFF, N. (1966): Orthogonal rotation to congruence. Psychomeirika, 31, 33–42.
COMMANDEUR, J.J.F., GROENEN, P.J.F. and MEULMAN, J.J. (1999): A distance-based variety of nonlinear multivariate data analysis, including weights for object and variables. Psychometrika, 64, 169–186.
EFRON, B. and TIBSHIRANI, R.J. (1993): An introduction to the bootstrap. New York, Chapman and 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.
KIERS, H.A.L. (2004): Bootstrap confidence intervals for three-way methods. Journal of Chemometrics, 18, 22–36.
LINTING, M., GROENEN, P.J.F. and MEULMAN, J.J. (2005): Stability of nonlinear principal components analysis by CatPCA: An empirical study. Submitted for publication.
LUNDY, M.E., HARSHMAN, R.A. and KRUSKAL, J.B. (1989): A two-stage procedure incorporating good features of both trilinear and quadrilinear models. In R. Coppi and S. Bolasco (Eds.) Multiway Data Analysis, Amsterdam, Elsevier.
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 Unpublished technical report, University of Leiden, The Netherlands.
TIMMERMAN, M.E., KIERS, H.A.L., and SMILDE, A.K. (2005): Bootstrap confidence interval in principal component analysis. Manuscript submitted for publication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Heidelberg
About this paper
Cite this paper
Kiers, H.A.L., Groenen, P.J.F. (2006). Visualizing Dependence of Bootstrap Confidence Intervals for Methods Yielding Spatial Configurations. In: Zani, S., Cerioli, A., Riani, M., Vichi, M. (eds) Data Analysis, Classification and the Forward Search. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35978-8_14
Download citation
DOI: https://doi.org/10.1007/3-540-35978-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35977-7
Online ISBN: 978-3-540-35978-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)