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4 - R-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

In this chapter we describe various methods suitable for studying the interrelationships among variables – so–called R-mode methods. In contrast, we treat in Chapter 5 Q-mode methods, which are designed for the study of interrelationships among objects.

In Chapter 3, we discussed the purposes, concepts, models, and terminology of factor analysis, a discussion that was put forward in terms of the population properties of the models. In practice, the data we have at our disposal consist of a sample drawn from the population. In the data matrix X, of order N × p, the rows constitute a random sample of observations from the population. From X one can compute the sample covariance matrix S, as we showed in Chapter 2. The statistical problem then is how does one go about estimating the population model from the data in X or S? In terms of the concepts of Chapter 3, we have the random case. The approach taken is that of fitting the population model to the data of the sample. However, even in the fixed case we need to fit a model to the data, since X or S will be approximated by matrices of lower rank. Some of the results are the same for the fixed and random cases. In the fixed case we are usually interested in estimating both the factor loadings matrix A and the factor scores matrix F, whereas in the random case, we are usually only interested in A and perhaps the covariance matrix Φ of the factors.

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Publisher: Cambridge University Press
Print publication year: 1993

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  • R-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/CBO9780511524882.007
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  • R-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/CBO9780511524882.007
Available formats
×

Send book to Google Drive

To send 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 sending content to Google Drive.

  • R-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/CBO9780511524882.007
Available formats
×