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*To*: ngalwey@cyllene.uwa.edu.au*Subject*: Re: units as a model term*From*: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>*Date*: Wed, 16 Dec 1998 08:22:25 +1100 (EST)*Cc*: asreml@ram.chiswick.anprod.csiro.au*Reply-To*: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>*Sender*: asreml-owner@ram.chiswick.anprod.csiro.au

Dear Nick, I have lost the connection but does this help? The standard AR1 process is defined as E_i = r.E_{i-1} + c.Ri the ith error is r times the previous error + c times a new independent error. The term 'nugget' refers to an extra independent error term - additional to the above. So if V = Var(E) = variance of the process it equals r^2 V + c^2 (for R_i independent standard normal) rearranging V = c^2 / (1-r^2) where c^2 is the innovation variance and r is the autocorrelation. Check this with a time series book but I think I have it correct. It seems you are calling c^2 the 'nugget' variance but the nugget variance is an extra (additional) variance term. So, without a nugget variance, the covariance of a series of points is given by V[ 1 r r^2 r^3 r^4 ...] If we add another Nugget variance say N the covariance becomes V+N Vr Vr^2 Vr^3 Vr^4 ... So the lag 1 correlation actually becomes Vr/(V+N) the lag2 correlation becomes Vr^2 /(V+N) So if V=2, r=.5, N=3 the Covariance sequence is 5 1 .5 .25 .125 ... This can only approximately be equated to a simple AR sequence with V=5 and r=0.2 giving 5 1 .2 .04 .008 What usually happens in fitting models in ASREML is that we start without a nugget variance. Then we might get V=5, r=.2 Then we add a nugget variance and get maybe N=3, V=2, r=0.5 This typically changes all variance parameters because they are expressed relative to V, not V+N, even though the difference in the model is largely in the covariance at lags 2 and 3. I hope this makes it a little clearer. Arthur > Date: Tue, 15 Dec 1998 17:28:50 +0800 > X-Sender: ngalwey@cyllene.uwa.edu.au > Mime-Version: 1.0 > To: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au> > From: "N.W. Galwey" <ngalwey@cyllene.uwa.edu.au> > Subject: Re: units as a model term > > Dear Arthur, > > I think we're going to have to discuss this some more face to face > before I understand it fully. I want the units term to give me the "new > bit" of the error for each observation (i.e. the bit that isn't correlated > with observations earlier in the series), which I'm identifying, perhaps > incorrectly, with the nugget. Yes, I have a feeling that that is incorrect. > > Hmm. > > Best wishes, > > Nick > _____________________________________________________________________ > N.W. Galwey, > Faculty of Agriculture, > University of Western Australia, > Nedlands, WA 6709, Australia. > > Tel.: +61 9 380 1959 (direct line) > +61 9 380 2554 (switchboard) > Fax: +61 9 380 1108 > <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Arthur Gilmour PhD email: Arthur.Gilmour@agric.nsw.gov.au Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899 NSW Agriculture <61> 2 6391 3922 Orange Agricultural Institute telephone work: <61> 2 6391 3815 Forest Rd, ORANGE, 2800, AUSTRALIA home: <61> 2 6362 0046 ASREML is still free by anonymous ftp from pub/aar on ftp.res.bbsrc.ac.uk or point your web browser at ftp://ftp.res.bbsrc.ac.uk/pub/aar/ To join the asreml discussion list, send the message subscribe to asreml-request@chiswick.anprod.CSIRO.au The address for messages to the list is asreml@chiswick.anprod.CSIRO.au Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml <> <> <> <> <> <> <> "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord." Romans 6:23 <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> -- Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml

**Follow-Ups**:**Re: nugget effect***From:*Vincenzo Matassa <s185152@student.uq.edu.au>

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