[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
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