RE: R-square statistic

# RE: R-square statistic

```Note that Genstat does not give the R-square statistic, but does give a
closely similar statistic summarising the goodness of fit:

percent variance accounted for = (MS(Total) - MS(Resid))/MS(Total)

where

MS(Total) = SS(Total)/DF(Total).

I think the reasoning is that R-square is misleading, as it inevitably
increases as the number of terms in the model increases, being based on sums
of squares rather than mean squares.

Percent variance accounted for is an exactly analogous calculation, but
based on mean squares.   Still, there is a problem in that the expected
value of MS(Total) is influenced not only by the extent to which the model
explains variation in the response variable, but also by the design of the
experiment, for instance the number of replications of each level of a
treatment factor.   I think the Genstat people would say that for this
reason it is better to compare variance components.   Which is all very well
for random effects, but what do you do with fixed effects...?

Nick Galwey

> -----Original Message-----
> From: asreml-owner@lamb.chiswick.anprod.csiro.au
> [mailto:asreml-owner@lamb.chiswick.anprod.csiro.au]On Behalf Of Arthur
> Gilmour
> Sent: Monday, August 07, 2000 6:47 AM
> Cc: asreml@chiswick.anprod.csiro.au
> Subject: Re: R-square statistic
>
>
> Dear Haja,
>
> ASREML does not report an Rsqu value but in many cases it will not
> be difficult to work one out from the ANOVA table when the first term
> is mu and there are no fixed effects absorbed (in the SPARSE equations).
>
> Ignoring the mu line, calculate the relative variance accounted
> in the model
> as the sum of products of df x R-incr.  The relative error variance
> is the error DF so R-square
>
>               Relative Model Variance
>               -----------------------
>               SUm of both components.
>   E.g.  in shf example [9.2]
>
>   Anova is    mu      1    853.96
>               c(var) 24     13.02
>
>               Error 125
>
>               RMV = 24*13.02 = 312.48
>
>               So R^2  is   312.48/(125 +312.48)   = 0.714
>
>   Note that Rsqu is a concept from fixed effect models and it is not
>   obvious to me how it should be defined in multistrata mixed models.
>
>   You can of course do the same calculation for GLMM models but I am
>   not aware of this being widely used and its meaning is a little less
>   direct becasue there it is with respect to a working variable
>   which changes as the model changes so has a moving basis.
>
>
>   Arthur
>
>
> > X-Authentication-Warning: lamb.chiswick.anprod.csiro.au:
> petidomo set sender
> to asreml-owner@lamb.chiswick.anprod.csiro.au using -f
> > To: asreml@chiswick.anprod.csiro.au
> > Date: Fri, 4 Aug 2000 11:29:58 +0100
> > Subject: R-square statistic
> >
> > Dear ASREML'ers,
> > 	A very simple question and sorry if this has been clarified before.
> > What is the equivalent of R-square (Multiple Correlation
> Coefficient) in
> > ASREML-GLMM and how to get this ? -something that tells us about
> > the adequacy of the model fitted, with effect of mean of y eliminated ?
> > 	I am not sure if testing significance of 'fixed' or
> 'random' effect in
> the
> > model would neccssarily lead to similar statistic, as they
> don't give us
> > any idea about the appropriateness of the whole model itself ?
> > Haja
> > --
> > Asreml mailinglist archive:
http://www.chiswick.anprod.csiro.au/lists/asreml

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Arthur Gilmour PhD                  mailto:Arthur.Gilmour@agric.nsw.gov.au
Principal 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

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