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Estimating structural equation models with non‐normal variables by using transformations

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  • Kees van Montfort
  • Ab Mooijaart
  • Frits Meijerink

Abstract

We discuss structural equation models for non‐normal variables. In this situation the maximum likelihood and the generalized least‐squares estimates of the model parameters can give incorrect estimates of the standard errors and the associated goodness‐of‐fit chi‐squared statistics. If the sample size is not large, for instance smaller than about 1000, asymptotic distribution‐free estimation methods are also not applicable. This paper assumes that the observed variables are transformed to normally distributed variables. The non‐normally distributed variables are transformed with a Box–Cox function. Estimation of the model parameters and the transformation parameters is done by the maximum likelihood method. Furthermore, the test statistics (i.e. standard deviations) of these parameters are derived. This makes it possible to show the importance of the transformations. Finally, an empirical example is presented.

Suggested Citation

  • Kees van Montfort & Ab Mooijaart & Frits Meijerink, 2009. "Estimating structural equation models with non‐normal variables by using transformations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 213-226, May.
    • Handle: RePEc:bla:stanee:v:63:y:2009:i:2:p:213-226
    DOI: 10.1111/j.1467-9574.2009.00420.x
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    References listed on IDEAS

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    1. Van Montfort, Kees & Mooijaart, Ab & De Leeuw, Jan, 1989. "Estimation of regression coefficients with the help of characteristic functions," Journal of Econometrics, Elsevier, vol. 41(2), pages 267-278, June.
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    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. Bengt Muthén, 1984. "A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 115-132, March.
    5. Jeffrey J. Hoogland & Anne Boomsma, 1998. "Robustness Studies in Covariance Structure Modeling," Sociological Methods & Research, , vol. 26(3), pages 329-367, February.
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