Acta Oeconomica Pragensia
Acta Oeconomica Pragensia
Acta Oeconomica Pragensia
Vědecký časopis Vysoké školy ekonomické v Praze

Acta Oeconomica Pragensia 1/2011

Srovnání metod pro redukci dimenzionality aplikovaných na ordinální proměnné

Comparison of Dimensionality Reduction Methods Applied to Ordinal Variables

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Lukáš Sobíšek, Hana Řezanková

Questionnaire survey data are usually characterized by a great amount of ordinal variables. For multivariate analysis, it is suitable to reduce task dimensionality. The aim of this paper is a comparison of the results obtained by the analysis of data files with ordinal variables using selected methods for dimensionality reduction. The results are in the form of individual component values (e.g. factor loadings). For better interpretation and comparability, these component values were consequently analyzed by fuzzy clustering. On the basis of the obtained clusters of variables, we determined the optimal number of dimensions. We applied silhouette and Dunn´s partition coeffi cients. Furthermore, we tried to merge the results received by individual methods on the basis of the sCSPA technique (soft version of cluster-based similarity partitioning algorithm). We considered groups of different methods and searched the best solution. The problems are illustrated by means of two real data fi les obtained from questionnaire surveys. We used SPSS, STATISTICA, Latent GOLD and S-PLUS systems.

Klíčová slova / Keywords: categorical principal component analysis, discrete factor analysis, fuzzy cluster analysis, latent class cluster models, multidimensional scaling

JEL klasifikace / JEL Classification: C38

BARTHOLOMEW, D. J.; STEELE, F. et al. 2002. The Analysis and Interpretation of Multivariate Data for
Social Scientists. Boca Raton : Chapman & Hall/CRC, 2002. ISBN 1-58488-295–6.
CLIFF, N. 1996. Orthogonal rotation to congruence. Psychometrika. 1996, vol. 31, s. 33–42.
DE LEEUW, J.; YOUNG, F. W.; TAKANE, Y. 1976. Additive structure in qualitative data: An alternating
least squares method with optimal scaling features. Psychometrika. 1976, vol. 41, s. 471–503.
HÄRDLE, W.; SIMAR, L. 2007. Applied Multivariate Statistical Analysis (Second edition). Berlin; Heidelberg;
New York : Springer, 2007. ISBN 978-3-540-72243-4.
HEBÁK, P.; HUSTOPECKÝ, J. et al. 2007. Vícerozměrné statistické metody [3]. 2. vyd. Praha : Informatorium,
2007. ISBN 978-80-7333-001-9.
IBM SPSS Statistics, Help, Algorithms [online]. On-line manuál. [cit. 2011-01-16]. www.
KAISER, H. F. 1985. The varimax criterion for analytic rotation in factor analysis. Psychometrika. 1985,
vol. 23, s. 187–200.
MARDIA, K. V.; KENT, J. T.; BIBBY, J. M. 1979. Multivariate Analysis. Duluth, London : Academic Press,
1979. ISBN 0-12-471252-5.
MOULISOVÁ M. 2009. Výzkum percepce policisty. Kriminalistika. 2009, roč. 42, č. 1, s. 56–71.
PUNERA, K.; GHOSH, J. 2007. Soft cluster ensembles. In OLIVEIRA, J. V.; PEDRYCZ, W. (eds.). Advances
in Fuzzy Clustering and Its Applications. Chichester : John Wiley & Sons, 2007, s. 69–91. ISBN
ŘEZANKOVÁ, H.; HÚSEK, D.; SNÁŠEL, V. 2009. Shluková analýza dat. 2. vyd. Praha : Professional
Publishing, 2009. ISBN 978-80-86946-26-9.
ŘEZANKOVÁ, H.; HÚSEK, D.; RYŠÁNKOVÁ, M. 2010. Grouping ordinal variables by using fuzzy cluster
analysis. In SMTDA 2010 – Stochastic Modeling Techniques and Data Analysis. Chania : Swets,
2010, s. 83.
TORGERSON, W. S. 1958. Theory and Methods of Scaling. New York : John Wiley & Sons, 1958.
VALJENT, Z. 2010. Aktivní životní styl vysokoškoláků (studentů FEL ČVUT v Praze). Praha : FEL ČVUT,
2010. ISBN 978-80-01-04669-2.
VERMUNT, J. K.; MAGIDSON, J. 2002. Latent class cluster analysis. In HAGENAARS, J. A.;
McCUTCHEON, A. L. (eds.). Applied Latent Class Analysis. Cambridge : Cambridge University
Press, 2002, s. 89–106. ISBN 0-521-59451-0.
VERMUNT, J. K.; MAGIDSON, J. 2005. Technical Guide for Latent GOLD 4.0: Basic and Advanced
[online]. Statistical Innovations Inc., Belmont Massachusetts, 2005. [cit. 2011-01-16].