# [R] Test for equality of coefficients in multivariate multiple regression

Andrew Robinson A.Robinson at ms.unimelb.edu.au
Wed Jul 19 03:51:44 CEST 2006

```Hi Uli,

I suggest that you try to rewrite the model system into a single
mixed-effects model, which would allow direct parameterization of the
tests that you're interested in.  A useful article, which may be
overkill for your needs, is:

Hall, D.B. and Clutter, M. (2004). Multivariate multilevel nonlinear
mixed effects models for timber yield predictions,  Biometrics, 60:
16-24.

See the publications link on Daniel Hall's website:

http://www.stat.uga.edu/~dhall/

Cheers

Andrew

On Tue, Jul 18, 2006 at 08:15:12PM +0200, Ulrich Keller wrote:
> Hello,
>
> suppose I have a multivariate multiple regression model such as the
> following:
>
>  > DF<-data.frame(x1=rep(c(0,1),each=50),x2=rep(c(0,1),50))
>  > tmp<-rnorm(100)
>  > DF\$y1<-tmp+DF\$x1*.5+DF\$x2*.3+rnorm(100,0,.5)
>  > DF\$y2<-tmp+DF\$x1*.5+DF\$x2*.7+rnorm(100,0,.5)
>  > x.mlm<-lm(cbind(y1,y2)~x1+x2,data=DF)
>  > coef(x.mlm)
>                     y1        y2
> (Intercept) 0.07800993 0.2303557
> x1          0.52936947 0.3728513
> x2          0.13853332 0.4604842
>
> How can I test whether x1 and x2 respectively have the same effect on y1
> and y2? In other words, how can I test if coef(x.mlm)[2,1] is
> statistically equal to coef(x.mlm)[2,2] and coef(x.mlm)[3,1] to
> coef(x.mlm)[3,2]? I looked at linear.hypothesis {car} and glh.test
> {gmodels}, but these do not seem the apply to multivariate models.
> Thank you in advance,
>
> Uli Keller
>
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--
Andrew Robinson
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
Email: a.robinson at ms.unimelb.edu.au         http://www.ms.unimelb.edu.au

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