Recovering the Metric Structure in Ordinal Data: Linear Versus Nonlinear Principal Components Analysis

Recovering the Metric Structure in Ordinal Data: Linear Versus Nonlinear Principal Components... Two techniques for data reduction as part of the SPSS package are compared in a Monte Carlo study: principal components analysis (PCA) and nonlinear principal components analysis (NPCA). The relative performance of these techniques in recovering the component scores underlying subjects' scores on observed ordinal variables is studied for two-dimensional spaces. The relative performance is examined as a function of (a) the sample size, (b) the number of categories in the variables, (c) the amount of measurement error, (d) the type of nonlinearity in the data, and (e) the degree of heterogeneity of the marginal distributions of the variables. As expected, when the sample size increases the performance of NPCA improves when compared to PCA. For the range of values considered, there is no effect of the number of categories on the relative performance of PCA and NPCA. For the other factors the effects are more complicated: adding error does not affect PCA as strongly as NPCA, as expected, but not for heterogeneously distributed variables for a particular form of nonlinearity, in which case NPCA becomes more appropriate. PCA appears to outperform NPCA for linear data, but also for a substantial number of nonlinear data sets. Quality & Quantity Springer Journals

Recovering the Metric Structure in Ordinal Data: Linear Versus Nonlinear Principal Components Analysis

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Kluwer Academic Publishers
Copyright © 2001 by Kluwer Academic Publishers
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
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