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*To*: "asreml@chiswick.anprod.csiro.au" <asreml@chiswick.anprod.csiro.au>*Subject*: RE: Correlations greater than 1*From*: Bruce Southey <southey@uiuc.edu>*Date*: Mon, 17 Apr 2000 10:26:30 -0500*Reply-To*: bsouthey@bigfoot.com*Sender*: asreml-owner@lamb.chiswick.anprod.csiro.au

Hi Kim, I think that correlations reported by ASREML would be rounding errors. You will get slightly different answers if you truncate or round the (co)variance estimates. For some traits, values near one are expected but other cases it may illustrate a bigger issue. All values should be reported as the actual value - although it is very much like how negative estimates of variance were truncated at zero when reported. This allows the readers to make their own mind about the true value weighted by have you describe the results. The issue of parameter space and land of no constraint have varying context. I am presuming your query relates to the computational aspects. By standard definition, variances are bounded by zero and plus infinity, covariances are bounded by minus and plus infinity but correlations are defined between minus one and plus one. Further, there are additional constraints that depend on model imposed such as genetic models as the heritability is defined between zero and one. For example, a sire model forces a particular constraint on residual variance. Therefore, constraints are required so that estimates are within their associated parameter spaces. The vast majority of methods (and the associated computational algorithms) to estimate variance components do not account for these constraints. For example, ANOVA permits negative estimates of variance components. An additional aspect is the type of algorithm used. Use of second-derivative methods are not guaranteed to converge and may converge to a local maximum. Most maximum likelihood methods usually only refer only to the variance components such that these remain in the parameter space. But does not guarantee that the correlations are within the parameter space. I believe that most programs attempt to re-estimate the (co)variance components if the correlations are out of the parameter space. But generally these end up with estimates on the boundary space hence correlations around +/-1. It is questionable if these are real values, at a local maximum or due to a lack of sufficient information. Hence, it is user beware and user be knowledgeable of the data, model and method. I do not know how ASREML implements the !GP option. However, I don't understand the concern about biased estimates because maximum likelihood is biased in the first place! Hope this helps, Bruce -- Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml

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