The fit of graphical displays to patterns of expectations

Moonseong Heo, K. Ruben Gabriel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Graphical displays of multivariate data often clearly exhibit features of the expectations even though the data themselves are poorly fitted by the displays. Thus, it often occurs that ordinations and biplots that poorly fit the sample data still reveal salient characteristics such as clusters of similar individuals and patterns of correlation. This paper provides an explanation of this seemingly paradoxical phenomenon and shows that when many variables are analyzed, the common measure of goodness of fit of a lower rank approximation often seriously underestimates the closeness of the fit to underlying patterns. The paper also provides some guidelines on better estimates of the latter goodness of fit.

Original languageEnglish (US)
Pages (from-to)47-67
Number of pages21
JournalComputational Statistics and Data Analysis
Issue number1
StatePublished - Mar 28 2001


  • Biplots
  • Goodness of fit
  • Graphical displays
  • Multivariate analysis
  • Rank

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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