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

[Andrew Robinson]

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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
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