Date: Thu, 20 Mar 2008 11:19:20 +0100 "Linting, Marielle" "SPSSX(r) Discussion" "Linting, Marielle" Bootstrap in CATPCA: announcement text/plain; charset="us-ascii"

Dear listers, Now available on DevCentral is a nonparametric bootstrap procedure for the CATPCA program from the SPSS Categories module. This procedure is used to perform a bootstrap study with 1000 bootstrap samples (by default) on a data set specified by the user, on which a two-dimensional PCA is performed. Although this procedure has been developed for nonlinear PCA (CATPCA) which offers provisions for analyzing (possibly) nonlinearly related variables of all types of measurement level, it can be applied to data sets with only linearly related numeric variables as well (by specifying a numeric analysis level for all variables in the data set and using the discretization option "multiplying"). A user's guide is provided along with the macro files to run the procedure. Below, a somewhat more elaborate description of the general purpose of the bootstrap in CATPCA is given.

In the daily research practice, data often do not meet the assumptions made by the traditional analysis methods, such as (multivariate) normality or numeric measurement levels. In such situations, multivariate categorical analysis techniques might be more effective. Nonlinear principal components analysis (nonlinear PCA), performed by CATPCA in the Categories module, is such a technique that has been developed as a nonlinear alternative to standard linear PCA, and can be used to explore the correlational structure between different types of variables (nominal, ordinal, and numeric) that may be nonlinearly related to each other. As PCA does not make particular assumptions about the distributions of the variables at hand, it does not seem theoretically sensible to apply standard (asymptotic) formulas for statistical inference. Therefore, in order to bring nonlinear PCA beyond its exploratory reputation, there is a need for easily applicable methods for performing inference on the elements of the nonlinear PCA solution without making prior assumptions about the data. For this purpose, the nonparametric bootstrap procedure mentioned above has been developed that establishes the stability of the nonlinear PCA solution, paying special attention to the graphical representation of the results. Bootstrap results for the eigenvalues, component loadings, and component scores are displayed by confidence ellipses, and results for the quantified variables are displayed by confidence intervals.

More information on the CATPCA procedure, along with an illustrative example, can be found in: Linting, M., Meulman, J. J., Groenen, P. J. F., & Van der Kooij, A. J. (2007). Nonlinear Principal Components Analysis: Introduction and application. Psychological Methods, 12, 336-358.

The exact procedure used to obtain, represent, and interpret the bootstrap results is described in an accompanying paper: Linting, M., Meulman, J. J., Groenen, P. J. F., & Van der Kooij, A. J. (2007). Stability of Nonlinear Principal Components Analysis: An empirical study using the balanced bootstrap. Psychological Methods, 12, 359-379.

*********************************************************** M. Linting Data Theory Group Faculty of Social and Behavioral Sciences Leiden University The Netherlands email: linting@fsw.leidenuniv.nl homepage: http://www.datatheory.nl/pages/linting.html ***********************************************************

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