A Least-Squares Solution for Correlation Structure Analysis with Fisher's Z-Transformation

Research output: Contribution to journalArticle

Abstract

The purpose of this study is to propose a least-squares method for parameter estimation using Fisher's z-transformation in correlation structure analysis. An advantage of this method in comparison with the unweighted least squares method (ULS) is that the residuals are normally distributed and their variances are homogeneous. A numerical example is given for factor analysis by using the data of Spearman (1904). Through the results of computer simulations in higher-order factor analysis, this method is shown to have less significant errors of parameter estimates than the ULS.

Original languageEnglish
Pages (from-to)67-70
Number of pages4
JournalJapanese Journal of Educational Psychology
Volume37
Issue number1
DOIs
Publication statusPublished - 1989
Externally publishedYes

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Least-Squares Analysis
Statistical Factor Analysis
factor analysis
computer simulation
Computer Simulation

Keywords

  • computer simulation
  • correlation structure analysis
  • Fisher's z-transformation
  • higher-order factor analysis
  • least-squares method

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology

Cite this

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abstract = "The purpose of this study is to propose a least-squares method for parameter estimation using Fisher's z-transformation in correlation structure analysis. An advantage of this method in comparison with the unweighted least squares method (ULS) is that the residuals are normally distributed and their variances are homogeneous. A numerical example is given for factor analysis by using the data of Spearman (1904). Through the results of computer simulations in higher-order factor analysis, this method is shown to have less significant errors of parameter estimates than the ULS.",
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AB - The purpose of this study is to propose a least-squares method for parameter estimation using Fisher's z-transformation in correlation structure analysis. An advantage of this method in comparison with the unweighted least squares method (ULS) is that the residuals are normally distributed and their variances are homogeneous. A numerical example is given for factor analysis by using the data of Spearman (1904). Through the results of computer simulations in higher-order factor analysis, this method is shown to have less significant errors of parameter estimates than the ULS.

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