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5 - Q-Mode Methods

Published online by Cambridge University Press:  12 November 2009

Richard A. Reyment
Affiliation:
Uppsala Universitet, Sweden
K. G. Jvreskog
Affiliation:
Uppsala Universitet, Sweden
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Summary

INTRODUCTION

An objective of many investigations is to classify a sample of objects (rock specimens, fossils, water samples, environments, etc.) on the basis of several properties, Specimens, Q-mode analysis, as first applied in geology by Imbrie (1963), is a valuable aid in doing this in cases where there are a large number of objects and, especially, where there is little a–priori knowledge of the significance of the constituents. The concept of Q-mode analysis was first developed by psychologists and then by biologists.

Q-mode analysis are designed to portray interrelationships between objects, just as in R-mode analyses interrelationships between variables are analyzed. To a certain extent, factor scores derived from R-mode analysis provide a means of describing interobject relationships; however, these associations are not usually based on a suitable measure of interobject similarity. That is, the covariance or correlation may not be the best criterion by which to judge the degree of similarity between two objects.

The mainstay of Q-mode factor analysis lies with the definition of interobject similarity. Once a suitable mathematical definition of this similarity coefficient has been established, it is possible to assemble an N × N similarity matrix containing the degree of similarity between all possible pairs of N objects. When N is large, this matrix will contain many elements and finding its rank by eigenanalysis may provide a means of adequately describing the objects in terms of fewer basic dimensions than original variables.

We describe here two methods of Q-mode analysis. The Imbrie Q-mode method defines similarity with respect to the proportions of constituents.

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Publisher: Cambridge University Press
Print publication year: 1993

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  • Q-Mode Methods
  • Richard A. Reyment, Uppsala Universitet, Sweden, K. G. Jvreskog, Uppsala Universitet, Sweden
  • Book: Applied Factor Analysis in the Natural Sciences
  • Online publication: 12 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524882.008
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  • Q-Mode Methods
  • Richard A. Reyment, Uppsala Universitet, Sweden, K. G. Jvreskog, Uppsala Universitet, Sweden
  • Book: Applied Factor Analysis in the Natural Sciences
  • Online publication: 12 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524882.008
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Q-Mode Methods
  • Richard A. Reyment, Uppsala Universitet, Sweden, K. G. Jvreskog, Uppsala Universitet, Sweden
  • Book: Applied Factor Analysis in the Natural Sciences
  • Online publication: 12 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511524882.008
Available formats
×