Abstract
Multivariate Analysis, like canonical correlation or principal component analysis with a mix of metric, nominal and ordinal data can be done by the classic method in combination with an optimal scaling technique described by (1981) and others. Variables with even more complex information levels, like hierachies, lattice orders, etc. are usually described by distances, but because distances have no directions and are rescaled by a different rescaling procedure, they cannot be compared equivalently with metric, nominal or ordinal variables. Here a method is proposed with fully generalizes the above mentioned methods to a set of variables of any above mentioned kind.
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
BURG, E. van der and DE LEEUW, J. (1983): Non-linear canonical correlation. British Journal of Mathematical and Statistical Psychology, 36, 1983, p. 54–80.
HANSOHM, J. (1987): Die Behandlung qualitativer Datenstrukturen in quantitativen Analysemethoden durch das Prinzip der optimalen Skalierung. Lang, Frankfurt, New York.
HANSOHM, J. (1988): Some Properties of the Normed Alternating Least Squares (ALS) Algorithm. Optimization, 19, 1988, Vol. 5, p. 683–691.
KRUSKAL, J.B. (1964a): Multidimensional Scaling by Optimizating Goodness of Fit to a Nonmetric Hypothesis. Psychometrika, 29, 1964, p. 1–27.
KRUSKAL, J.B. (1964b): Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika, 29, 1964, p. 115–129.
KRUSKAL, J.B. and CARMONE (1968): Use and Theory of MONANOVA — a Program to Analyze Factorial Experiments by Estimating Monotone Transformations of the Data. unpublished paper, Bell Laboratories, 1968.
OPITZ, O. (1980): Numerische Taxonomie. UTB Betriebswirtschaftslehre, Gustav Fischer, 1980, Stuttgart, New York.
YOUNG, F.W. (1975): Methods for Describing Ordinal Data with Cardinal Models. Journal of Mathematical Psychology, 12, 1975, 416–536.
YOUNG, F. W., DE LEEUW, J., TAKANE, Y. (1976): Regression with Qualitative and Quantitative Variables: An Alternating Least Squares Method with Optimal Scaling Features. Psychometrika, 41, 4, 1976, 505–529.
YOUNG, F.W. (1981): Quantitative Analysis of Qualitative Data. Psychometrika, 46, 4, 1981, p. 357–388.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hansohm, J. (2003). Multivariate Analysis for Variables of Arbitrary Information Level. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-18991-3_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40354-8
Online ISBN: 978-3-642-18991-3
eBook Packages: Springer Book Archive