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Approximating Test Statistics Using Eigenvalue Block Averaging

Foldnes, Njål; Grønneberg, Steffen
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2474090
Date
2018
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Original version
Structural Equation Modeling: A Multidisciplinary Journal, 2018, 25(1),   10.1080/10705511.2017.1373021
Abstract
We introduce and evaluate a new class of approximations to common test statistics in structural equation modeling. Such test statistics asymptotically follow the distribution of a weighted sum of i.i.d. chi-square variates, where the weights are eigenvalues of a certain matrix. The proposed eigenvalue block averaging (EBA) method involves creating blocks of these eigenvalues and replacing them within each block with the block average. The Satorra–Bentler scaling procedure is a special case of this framework, using one single block. The proposed procedure applies also to difference testing among nested models. We investigate the EBA procedure both theoretically in the asymptotic case, and with simulation studies for the finite-sample case, under both maximum likelihood and diagonally weighted least squares estimation. Comparison is made with 3 established approximations: Satorra–Bentler, the scaled and shifted, and the scaled F tests.
Description
The accepted and peer reviewed manuscript to the article
Publisher
Taylor and Francis
Journal
Structural Equation Modeling: A Multidisciplinary Journal

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