The fit of graphical displays to patterns of expectations

Moonseong Heo, K. Ruben Gabriel

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume36
Issue number1
DOIs
StatePublished - Mar 28 2001
Externally publishedYes

Fingerprint

Graphical Display
Goodness of fit
Ordination
Display devices
Biplot
Low-rank Approximation
Multivariate Data
Display
Estimate
Closeness
Approximation

Keywords

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

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Computational Mathematics
  • Numerical Analysis
  • Statistics and Probability

Cite this

The fit of graphical displays to patterns of expectations. / Heo, Moonseong; Ruben Gabriel, K.

In: Computational Statistics and Data Analysis, Vol. 36, No. 1, 28.03.2001, p. 47-67.

Research output: Contribution to journalArticle

@article{5d5b1acfbeaa4a8396c21a7fdcdfd6e8,
title = "The fit of graphical displays to patterns of expectations",
abstract = "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.",
keywords = "Biplots, Goodness of fit, Graphical displays, Multivariate analysis, Rank",
author = "Moonseong Heo and {Ruben Gabriel}, K.",
year = "2001",
month = "3",
day = "28",
doi = "10.1016/S0167-9473(00)00016-5",
language = "English (US)",
volume = "36",
pages = "47--67",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - The fit of graphical displays to patterns of expectations

AU - Heo, Moonseong

AU - Ruben Gabriel, K.

PY - 2001/3/28

Y1 - 2001/3/28

N2 - 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.

AB - 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.

KW - Biplots

KW - Goodness of fit

KW - Graphical displays

KW - Multivariate analysis

KW - Rank

UR - http://www.scopus.com/inward/record.url?scp=0035961970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035961970&partnerID=8YFLogxK

U2 - 10.1016/S0167-9473(00)00016-5

DO - 10.1016/S0167-9473(00)00016-5

M3 - Article

VL - 36

SP - 47

EP - 67

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -