I would like to run an ANCOVA using car::Anova but cannot find out if there is a way to add a covariate only as a main effect (i.e., should not interact with anything).
As far as I understand ANCOVA, covariates are just another main effect added to the model (i.e., one more effect), thereby controlling for the overall additive influence of this covariate. Followingly, the covariate(s) do not interact with the other factors. However, I cannot add a variable to Anova that does not interact with the within-subject factors (i.e., my final model does not seem to ba an ANCOVA).
Let me illustrate my problem with an example from ?Anova. The OBrienKaiser data set has 2 between (treatment and gender) and 2 within (phase and hour) factors. Now lets assume we also recorded the age of the participants and would like to add it as a covariate to the any analysis.
require(car)
set.seed(1)
n.OBrienKaiser <- within(OBrienKaiser, age <- sample(18:35, size = 16, replace = TRUE))
# the next part is taken from ?Anova
# I only modified the mod.ok <- ... call by adding + age
phase <- factor(rep(c("pretest", "posttest", "followup"), c(5, 5, 5)), levels=c("pretest", "posttest", "followup"))
hour <- ordered(rep(1:5, 3))
idata <- data.frame(phase, hour)
mod.ok <- lm(cbind(pre.1, pre.2, pre.3, pre.4, pre.5, post.1, post.2, post.3, post.4, post.5,
fup.1, fup.2, fup.3, fup.4, fup.5) ~ treatment*gender + age, data=n.OBrienKaiser)
(av.ok <- Anova(mod.ok, idata=idata, idesign=~phase*hour, type = 3))
As the results show, the results contain interaction with the covariate age, namely of the within-subject (or repeated-measures) factors phase, hour and their interaction phase:hour:
Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.129 1.33 1 9 0.278
treatment 2 0.443 3.58 2 9 0.072 .
gender 1 0.305 3.95 1 9 0.078 .
age 1 0.054 0.52 1 9 0.490
treatment:gender 2 0.222 1.28 2 9 0.323
phase 1 0.418 2.87 2 8 0.115
treatment:phase 2 0.871 3.47 4 18 0.029 *
gender:phase 1 0.084 0.37 2 8 0.703
age:phase 1 0.393 2.59 2 8 0.136
treatment:gender:phase 2 0.545 1.69 4 18 0.197
hour 1 0.565 1.95 4 6 0.222
treatment:hour 2 0.580 0.72 8 14 0.676
gender:hour 1 0.310 0.68 4 6 0.633
age:hour 1 0.508 1.55 4 6 0.301
treatment:gender:hour 2 0.707 0.96 8 14 0.504
phase:hour 1 0.975 9.56 8 2 0.098 .
treatment:phase:hour 2 1.145 0.50 16 6 0.873
gender:phase:hour 1 0.693 0.56 8 2 0.770
age:phase:hour 1 0.974 9.40 8 2 0.100 .
treatment:gender:phase:hour 2 1.314 0.72 16 6 0.723
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
My question is: Can one run a ANCOVA with car::Anova and if so is there a way to specify this ANCOVA without any interaction of age?
Update (July 22, 2012): I asked this question on R-help, but so far no responses. If there are news, I will post it here.
I asked this question on R-help which started a helpful discussion with John Fox (later joined by Peter Dalgaard). Unfortunately it got split up into two threads: one, two.
The punchline is:
“The within-subjects contrasts are constructed by Anova() to be orthogonal in the row-basis of the design, so you should be able to safely ignore the effects in which (for some reason that escapes me) you are uninterested.” (John Fox)
So the answer to the question is: No one can’t, but it doesn’t matter because these interactions do not alter the other effects as they are orthogonal.