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Embedding common factors in a path model

  • Roderick P. McDonald
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 120)

Abstract

In models containing unobservable variables with multiple indicators--common factors, true scores--it seems to be common practice not to allow, except in special cases, nonzero covariances of residuals of indicators of the common factors and other variables in the model. Indeed, those models, such as LISREL and LISCOMP, that separate a “measurement” model from a “structural” model, exclude these by their defining matrix structure. Yet it is not at all obvious that such covariances should not be allowed, and it seems desirable to look for some explicit principles to apply to such cases, rather than settle the matter by default. This question will be examined in the context of the reticular action model. The following section sets out some necessary preliminaries from the case of path models without common factors, then section 3 treats the problem of embedding a block of common factors in a path model. Section 4 gives a numerical example.

Keywords

Common Factor Path Model Latent Trait True Score Precedence Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bollen, K.A. (1989). Structural equations with latent variables. N.Y.:Wiley.zbMATHGoogle Scholar
  2. Duncan, O.D. (1975). Introduction to structural equation models. N.Y.: Academic Press.zbMATHGoogle Scholar
  3. Fox, J. (1984). Linear statistical models and related methods. N.Y.:Wiley.zbMATHGoogle Scholar
  4. Fraser, C. & McDonald, R.P. (1988). COSAN: Covariance structure analysis. Multivariate Behavioral Research, 23, 263–265.CrossRefGoogle Scholar
  5. James, L.R., Mulaik, S.A., & Brett, J. M. (1982). Causal analysis: assumptions, models, and data. Beverley Hills: Sage.Google Scholar
  6. Kang, K.M. & Seneta, E. (1980). Path analysis; an exposition. In Krishnaiah, P.R., ed., Developments in statistics, vol. 3, N.Y.: Academic Press, pp. 19–49.Google Scholar
  7. Land, K.C. (1969). Priciples of path analysis. In Borgatta E.F. (Ed.), Sociological Methodology, PP.3–37.Google Scholar
  8. McArdle, J.J. & McDonald, R.P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of mathematical and statistical Psychology, 37, 234–251.zbMATHGoogle Scholar
  9. McDonald, R.P. (1981). The dimensionality of tests and items. British Journal of mathematical and statistical Psychology, 34, 100–117MathSciNetGoogle Scholar
  10. McDonald, R.P. (1985). Factor analysis and related methods. Hillsdale: Lawrence Erlbaum Associates, Ch. 4.Google Scholar
  11. McDonald, R.P. (in prep.) Haldane’s lungs: a case study in path analysis.Google Scholar
  12. Schmidt, P. (1982). Econometrics, in Encyclopedia of statistical Sciences, vol. 2, 441–451, N.Y.; Wiley.Google Scholar
  13. Wright, S. (1934). The method of path coefficients. Annals of mathematical Statistics, 5, 161–215.zbMATHCrossRefGoogle Scholar
  14. Wright, S. (1960). Path coefficients and path regressions: alternative or complementary concepts? Biometrics, $$, 189–202.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Roderick P. McDonald
    • 1
  1. 1.University of IllinoisUSA

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