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*To*: <asreml@chiswick.anprod.csiro.au>*Subject*: Sig test for variance components*From*: "N.W. Galwey" <ngalwey@cyllene.uwa.edu.au>*Date*: Fri, 8 Dec 2000 13:43:14 +0800*Sender*: asreml-owner@lamb.chiswick.anprod.csiro.au

In the ASREML manual, a method is given of testing the significance of a single variance component by calculating the difference between the residual log likelihoods from models with and without the component, then treating this as a chi-square statistic with 1 d.f. but multiplying the P-value by 0.5 (approximation of Stram and Lee, 1994). Can this method be extended to compare models that differ by >1 variance component? Here is an attempt to do so. The philosophy is that the chi-square statistic with 1 d.f. is the square of an underlying variable, on which we are conducting a 1-tailed test (just as F(1,nu2) is the square of t(nu2)), because only values at the right-hand end of the underlying variable would cause us to reject H0. Now, chi-square with 2 d.f. is similarly an integral of a bivariate distribution, in which only values in the upper right-hand quadrant would cause us to reject H0. And so on for higher numbers of d.f. Thus when p variance components are being added to the model, the difference in residual log likelihoods should be treated as a chi-square variable with p d.f., but the probability value obtained should be multiplied by 0.5 ** p. Comments, please. Nick Galwey _____________________________________________________________________ N.W. Galwey, Faculty of Agriculture, University of Western Australia, 35 Stirling Highway, Crawley. Western Australia 6009 Tel.: +61 8 9380 1959 (direct line) +61 8 9380 2554 (switchboard) Fax: +61 8 9380 1108 -- Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml

**Follow-Ups**:**Re: Sig test for variance components***From:*<southey@ux1.cso.uiuc.edu>

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