Nonlinear Principal Components Analysis With CATPCA: A Tutorial

This article is set up as a tutorial for nonlinear principal components analysis (NLPCA), systematically guiding the reader through the process of analyzing actual data on personality assessment by the Rorschach Inkblot Test. NLPCA is a more flexible alternative to linear PCA that can handle the analysis of possibly nonlinearly related variables with different types of measurement level. The method is particularly suited to analyze nominal (qualitative) and ordinal (e.g., Likert-type) data, possibly combined with numeric data. The program CATPCA from the Categories module in SPSS is used in the analyses, but the method description can easily be generalized to other software packages.

[1]  L. Guttman,et al.  The Quantification of a class of attributes : A theory and method of scale construction , 1941 .

[2]  I. Jolliffe,et al.  Nonlinear Multivariate Analysis , 1992 .

[3]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[4]  B. Price.  A First Course in Factor Analysis , 1993 .

[5]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[6]  J. Kruskal.  Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data , 1965 .

[7]  G. Meyer.  The Rorschach's factor structure: a contemporary investigation and historical review. , 1992, Journal of personality assessment.

[8]  Suzanne Winsberg,et al.  Monotone spline transformations for dimension reduction , 1983 .

[9]  Jacqueline J. Meulman,et al.  Statistical Significance of the Contribution of Variables to the PCA solution: An Alternative Permutation Strategy , 2011 .

[10]  Jacqueline J Meulman,et al.  Stability of nonlinear principal components analysis: an empirical study using the balanced bootstrap. , 2007, Psychological methods.

[11]  Willem J. Heiser,et al.  Principal Components Analysis With Nonlinear Optimal Scaling Transformations for Ordinal and Nominal Data , 2005 .

[12]  M. Hill,et al.  Nonlinear Multivariate Analysis. , 1990 .

[13]  Forrest W. Young,et al.  The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features , 1978 .

[14]  G. Meyer,et al.  A Replication of Rorschach and MMPI-2 Convergent Validity , 2000, Journal of personality assessment.

[15]  J. Exner,et al.  The Rorschach : a comprehensive system , 1974 .

[16]  R. Shepard.  Metric structures in ordinal data , 1966 .

[17]  Age K Smilde,et al.  Estimating confidence intervals for principal component loadings: a comparison between the bootstrap and asymptotic results. , 2007, The British journal of mathematical and statistical psychology.

[18]  Jacqueline J Meulman,et al.  Nonlinear principal components analysis: introduction and application. , 2007, Psychological methods.

[19]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[20]  Monica Th. Markus,et al.  Bootstrap confidence regions in nonlinear multivariate analysis , 1994 .

[21]  G. Meyer,et al.  Response frequency problems in the rorschach: clinical and research implications with suggestions for the future. , 1992, Journal of personality assessment.

[22]  R. Shepard,et al.  A nonmetric variety of linear factor analysis , 1974 .