TY - JOUR

T1 - Estimating structural equation models with non-normal variables by using transformations

AU - van Montfort, C.A.G.M.

AU - Mooijaart, A.

AU - Meijer, F.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

U2 - 10.1111/j.1467-9574.2009.00420.x

DO - 10.1111/j.1467-9574.2009.00420.x

M3 - Article

VL - 63

SP - 213

EP - 226

JO - Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research

JF - Statistica Neerlandica. Journal of the Netherlands Society for Statistics and Operations Research

SN - 0039-0402

IS - 2

ER -