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

C.A.G.M. van Montfort, A. Mooijaart, F. Meijer

    Research output: Contribution to JournalArticleAcademicpeer-review


    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. © 2009 VVS.
    Original languageEnglish
    Pages (from-to)213-226
    Number of pages14
    JournalStatistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research
    Issue number2
    Publication statusPublished - 2009


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