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

John Fox jfox at mcmaster.ca
Tue Jul 18 21:33:22 CEST 2006

```Dear Ulrich,

I'll look into generalizing linear.hypothesis() so that it handles
multivariate linear models.

Meanwhile, vcov(x.mlm) will give you the covariance matrix of the
coefficients, so you could construct your own test by ravelling
coef(x.mlm) into a vector.

I hope that this helps,
John

On Tue, 18 Jul 2006 20:15:12 +0200
Ulrich Keller <uhkeller at web.de> 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.
>
> Uli Keller
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--------------------------------
John Fox
Department of Sociology
McMaster University