Restricted principal components analysis for marketing research

Wayne S. DeSarbo, Robert E. Hausman, Jeffrey M. Kukitz

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

PurposePrincipal components analysis (PCA) is one of the foremost multivariate methods utilized in marketing and business research for data reduction, latent variable modeling, multicollinearity resolution, etc. However, while its optimal properties make PCA solutions unique, interpreting the results of such analyses can be problematic. A plethora of rotation methods are available for such interpretive uses, but there is no theory as to which rotation method should be applied in any given social science problem. In addition, different rotational procedures typically render different interpretive results. The paper aims to introduce restricted PCA (RPCA), which attempts to optimally derive latent components whose coefficients are integer-constrained (e.g.: {-1,0,1}, {0,1}, etc.). Design/methodology/approachThe paper presents two algorithms for deriving efficient solutions for RPCA: an augmented branch and bound algorithm for sequential extraction, and a combinatorial optimization procedure for simultaneous extraction of these constrained components. The paper then contrasts the traditional PCA-derived solution with those obtained from both proposed RPCA procedures with respect to a published data set of psychographic variables collected from potential buyers of the Dodge Viper sports car. FindingsThis constraint results in solutions which are easily interpretable with no need for rotation. In addition, the proposed procedure can enhance data reduction efforts since fewer raw variables define each derived component. Originality/valueThe paper provides two algorithms for estimating RPCA solutions from empirical data.

Original languageEnglish (US)
Pages (from-to)305-328
Number of pages24
JournalJournal of Modelling in Management
Volume2
Issue number3
DOIs
Publication statusPublished - Jan 1 2007

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All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Strategy and Management
  • Management Science and Operations Research

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