# [R] Multivariate LM: calculating F-values after calling linear.hypothesis

Dr. Christoph Scherber Christoph.Scherber at agr.uni-goettingen.de
Sat Jun 7 22:38:54 CEST 2008

```Dear R users,

I am analyzing several response variables (all scaled to [0;1]) using a
multivariate linear model.

After fitting the model, I set up a hypothesis matrix to test specific
contrasts for these response variables; for example: "a always increases
significantly more than b when regressed against x".

What I am stuck with now is how to calculate the correct F-values (and
against how many d.f. to test them) after calling linear.hypothesis from
the car package:

(assuming there are 80 observations)

##

mult=lm(cbind(a,b,c,d,e,f,g)~x)

summary(mult)
library(car)

P <- cbind(
c(-1,1,0,0,0,0,0),
c(-3,-3,6,6,-3,-3,0),
c(0,0,2,0,-1,-1,0),
c(0,0,-1,0,1,0,0))

P
[,1] [,2] [,3]
[1,]   -1   -3    0
[2,]    1   -3    0
[3,]    0    6    2
[4,]    0    6    0
[5,]    0   -3   -1
[6,]    0   -3   -1
[7,]    0    0    0

summary(mult)

linhyp=linear.hypothesis(mult, "x", P=P)

linhyp

Response transformation matrix:
[,1] [,2] [,3] [,4]
[1,]   -1   -3    0    0
[2,]    1   -3    0    0
[3,]    0    6    2   -1
[4,]    0    6    0    0
[5,]    0   -3   -1    1
[6,]    0   -3   -1    0
[7,]    0    0    0    0

Sum of squares and products for the hypothesis:
[,1]      [,2]       [,3]       [,4]
[1,]  0.06744438 -2.065499 -0.5790014  0.3233393
[2,] -2.06549912 63.256374 17.7320486 -9.9023380
[3,] -0.57900143 17.732049  4.9706540 -2.7758268
[4,]  0.32333928 -9.902338 -2.7758268  1.5501410

Sum of squares and products for error:
[,1]       [,2]      [,3]       [,4]
[1,]  4.4957632   1.084781  2.196134 -0.7621832
[2,]  1.0847809 173.494183 20.425963 -7.7303319
[3,]  2.1961336  20.425963  8.584237 -3.8182268
[4,] -0.7621832  -7.730332 -3.818227  2.3045286

1-pf(diag(linhyp2\$SSPH)/diag(linhyp2\$SSPE),1,79)
1-pt(sqrt(diag(linhyp2\$SSPH)/diag(linhyp2\$SSPE)),79)

##

The last two lines of code are what I am stuck with; I thought using
diag() on the SSPH and SSPE matrices should give me the sums of squares
for hypothesis and error; so division should yield the F values?

I would be most grateful for any help!

Best wishes
Christoph

--
Dr. Christoph Scherber
University of Goettingen
DNPW, Agroecology
Waldweg 26
D-37073 Goettingen, Germany
www.gwdg.de/~cscherb1

```