Comparison of Dimensionality Reduction Methods Applied to Ordinal Variables

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.