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How general is the Vale-Maurelli simulation approach?

Foldnes, Njål; Grønneberg, Steffen
Journal article, Peer reviewed
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Foldnes_Gronneberg_Psychometrika 2015.pdf (371.6Kb)
URI
http://hdl.handle.net/11250/2374516
Date
2015
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Original version
Psychometrika, 80(2015)4:1066-1083   10.1007/s11336-014-9414-0
Abstract
The Vale-Maurelli (VM) approach to generating non-normal mul-

tivariate data involves the use of Fleishman polynomials applied to an underly-

ing Gaussian random vector. This method has been extensively used in Monte

Carlo studies during the last three decades to investigate the nite-sample per-

formance of estimators under non-Gaussian conditions. The validity of con-

clusions drawn from these studies clearly depends on the range of distributions

obtainable with the VM method. We deduce the distribution and the copula

for a vector generated by a generalized VM transformation, and show that it

is fundamentally linked to the underlying Gaussian distribution and copula.

In the process we derive the distribution of the Fleishman polynomial in full

generality. While data generated with the VM approach appears to be highly

non-normal, its truly multivariate properties are close to the Gaussian case.

A Monte Carlo study illustrates that generating data with a di erent copula

than that implied by the VM approach severely weakens the performance of

normal-theory based ML estimates.The Vale-Maurelli (VM) approach to generating non-normal mul-

tivariate data involves the use of Fleishman polynomials applied to an underly-

ing Gaussian random vector. This method has been extensively used in Monte

Carlo studies during the last three decades to investigate the nite-sample per-

formance of estimators under non-Gaussian conditions. The validity of con-

clusions drawn from these studies clearly depends on the range of distributions

obtainable with the VM method. We deduce the distribution and the copula

for a vector generated by a generalized VM transformation, and show that it

is fundamentally linked to the underlying Gaussian distribution and copula.

In the process we derive the distribution of the Fleishman polynomial in full

generality. While data generated with the VM approach appears to be highly

non-normal, its truly multivariate properties are close to the Gaussian case.

A Monte Carlo study illustrates that generating data with a di erent copula

than that implied by the VM approach severely weakens the performance of

normal-theory based ML estimates.
Description
This is the authors' accepted and refereed manuscript to the article
Publisher
Springer
Journal
Psychometrika

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