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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

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

Loading next page...
 
/lp/springer_journal/recovering-the-metric-structure-in-ordinal-data-linear-versus-0PJzHOADyf
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1023/A:1004873031561
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Quality & QuantitySpringer Journals

Published: Oct 3, 2004

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off