# Re: [R] Test for equality of coefficients in multivariate multipleregression

From: Berwin A Turlach <berwin_at_maths.uwa.edu.au>
Date: Wed 19 Jul 2006 - 22:43:41 EST

G'day John,

>>>>> "JF" == John Fox <jfox@mcmaster.ca> writes:

```    JF> Simply stacking the problems and treating the resulting
JF> observations as independent will give you the correct
JF> coefficients, but incorrect coefficient variances
```
Yes, after Andrew's (off-list) answer I realised this too. If I am not mistaken, all variances/covariances should be off by a factor of 1/2 or something like that.

JF> and artificially zero covariances. Well, I must admit that I misread Ulrich's code for most of the day. I hadn't realised that the variable `tmp' introduces a correlation between `y1' and `y2' in his code:

> 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)

for some reason, my brain kept parsing this as generate *one* random intercept for y1 and *one* random intercept for y2, not that each individual observation has a random intercept. Under the model that my brain kept parsing, one would have zero covariances. :)

Now I understand why Andrew suggested the use of mixed models and would go down that way too. But I believe your approach is valid too.

JF> (BTW, it's a bit unclear to me how much of this exchange was     JF> on r-help,
Easy, all those that have r-help either in the TO: or CC: field. Those were Ulrich's original message and the answer by you and Andrew, I kept all my mails so far off-list.

JF> but I'm copying to r-help since at least one of Ulrich's     JF> messages referring to alternative approaches appeared there. Yes, I noticed that and answered off-list. In that message, if I read it correctly, he had confused Andrew and me.

JF> I hope that's OK.)
Sure, why not? :)

Cheers,

Berwin

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