ERIC Number: EJ775074
Record Type: Journal
Publication Date: 2007-Sep
Reference Count: N/A
Nonlinear Principal Components Analysis: Introduction and Application
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Koojj, Anita J.
Psychological Methods, v12 n3 p336-358 Sep 2007
The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.
Descriptors: Likert Scales, Computation, Statistical Analysis, Measurement Techniques, Computer Software
American Psychological Association. Journals Department, 750 First Street NE, Washington, DC 20002-4242. Tel: 800-374-2721; Tel: 202-336-5510; Fax: 202-336-5502; e-mail: email@example.com; Web site: http://www.apa.org/publications
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A