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*To*: "N.W. Galwey" <ngalwey@cyllene.uwa.edu.au>*Subject*: Re: Sig test for variance components*From*: <southey@ux1.cso.uiuc.edu>*Date*: Wed, 13 Dec 2000 08:11:38 -0600 (CST)*cc*: asreml@chiswick.anprod.csiro.au*In-Reply-To*: <000401c060d9$c20f5b90$54205f82@ps-ngalway.agric.uwa.edu.au>*Sender*: asreml-owner@lamb.chiswick.anprod.csiro.au

Hi, Self and Liang (1987) and Stram and Lee (1994; see 1995 for erratum) discuss many cases. The general case of Q versus Q+1 random effects is a 50:50 mixture of Chi-squared with Q+1 df and a Chi-squared with Q df. The multiplication by 0.5 is the case when Q=0 i.e. 50:50 mixture of Chi-squared with 0 df (point mass zero) and Chi-squared with 1 df. For Q versus Q+k, apart from special cases, you probably will not know the correct null distribution. Hope this helps, Bruce Southey On Fri, 8 Dec 2000, N.W. Galwey wrote: > 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 > -- Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml

**References**:**Sig test for variance components***From:*"N.W. Galwey" <ngalwey@cyllene.uwa.edu.au>

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