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Estimating structural equation models with non‐normal variables by using transformations
Author(s) -
Montfort Kees van,
Mooijaart Ab,
Meijerink Frits
Publication year - 2009
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2009.00420.x
Subject(s) - mathematics , statistics , transformation (genetics) , goodness of fit , maximum likelihood , estimating equations , biochemistry , chemistry , gene
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.