car::Anova - Can it be used for ANCOVA with repeated-measures factors.

contrasts(OBrienKaiser$gender)

Dear John,

thanks for your response. But if I simply ignore the unwanted effects, the estimates of the main effects for the within-subjects factors are distroted (rationale see below). Or doesn't this hold for between-within interactions?

Or put another way: Do you think this approach is the correct way of running an ANCOVA involving within-subject factors?

As far as I understand ANCOVA, the covariate(s) should only be additive factors and do not interact with the factors of interest:
"Suppose that differences in [the mean of the covariate] are due to sources of variation related to [the mean of the dependent variable], but not directly related to the treatment effects." (Winer, 1972, p. 753, the parts in squared bracktes exchange the mathematical symbols with the definition).

Best,
Henrik

PS: Showing that adding the interaction term massively changes the main effect for a between-factor:

# The ANCOVA:
Anova(lm(pre.1 ~ treatment + age, data = n.OBrienKaiser), type = 3)

Anova Table (Type III tests)

Response: pre.1
             Sum Sq Df F value Pr(>F)
(Intercept)    0.0  1    0.01   0.90
treatment      0.3  2    0.06   0.94
age            4.5  1    1.54   0.24
Residuals     34.9 12

# The ANOVA:
Anova(lm(pre.1 ~ treatment, data = n.OBrienKaiser), type = 3)

Anova Table (Type III tests)

Response: pre.1
             Sum Sq Df F value     Pr(>F)
(Intercept)  225.6  1   74.47 0.00000097 ***
treatment      1.1  2    0.17       0.84
Residuals     39.4 13
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

# The model with interaction
Anova(lm(pre.1 ~ treatment * age, data = n.OBrienKaiser), type = 3)

Anova Table (Type III tests)

Response: pre.1
               Sum Sq Df F value Pr(>F)
(Intercept)     3.01  1    1.40  0.264
treatment      13.71  2    3.18  0.085 .
age            11.56  1    5.37  0.043 *
treatment:age  13.37  2    3.11  0.089 .
Residuals      21.53 10
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Am 22.07.2012 16:59, schrieb John Fox:

Dear Henrik,

As you discovered, entering the covariate age additively into the between-subject model doesn't prevent Anova() from reporting tests for the interactions between age and the within-subjects factors. I'm not sure why you would want to do so, but you could simply ignore these tests.

I hope this helps,
  John

--------------------------------
John Fox
Senator William McMaster
   Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Henrik Singmann
Sent: July-21-12 1:29 PM
To: r-help at stat.math.ethz.ch
Subject: [R] car::Anova - Can it be used for ANCOVA with repeated-
measures factors.

Dear list,

I would like to run an ANCOVA using car::Anova with repeated measures
factors, but I can't figure out how to do it. My (between-subjects)
covariate always interacts with my within-subject factors.
As far as I understand ANCOVA, covariates usually do not interact with
the effects of interest but are simply additive (or am I wrong here?).

More specifically, I can add a covariate as a factor to the between-
subjects part when fitting the MLM that behaves like expected (i.e.,
does not interact with the other factors), but when calling Anova on
the model, I don't know how I can specify the between-within design
(i.e., which parts of the model should interact with the repeated
measures factors).

As far as I understand it, neither the idesign, icontrasts or imatrix
arguments, nor the linearHypothesis function can specify the within-
between design (as far as I get it they all specify the within or
intra-subject design, see John Fox's slides from User 2011:
http://web.warwick.ac.uk/statsdept/useR-
2011/TalkSlides/Contributed/17Aug_1705_FocusV_4-Multivariate_1-
Fox.pdf).

If this it is not possible using car::Anova, is there another way to
achiebve what I want or is it plainly wrong?
I have the feeling that using R's "New Functions for Multivariate
Analysis" (Dalgaard, 2007, R News) this could be possible, but some
advice on how, would be greatly appreciated, as this does not seem to
be the most straight forward way.

Below is an example using the car::OBrienKaiser dataset adding an age
covariate. The example is merely an adoption from ?Anova with miniml
changes and includes e.g. age:phase:hour which I don't want to have.

Note that I posted this question to stackoverflow two days ago
(http://stackoverflow.com/q/11567446/289572) and did not receive any
responses. Please excuse my "crossposting", but I think R-help may be
the better place.

Best,
Henrik

PS: I know that the posting guide says "No questions about contributed
packages" but there are some questions about car on R-help, so I
thought this would be the correct place.

###### Example follows #####

require(car)
set.seed(1)

n.OBrienKaiser <- within(OBrienKaiser, age <- sample(18:35, size = 16,
replace = TRUE))

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))

# Type II Repeated Measures MANOVA Tests: Pillai test statistic
                              # Df test stat approx F num Df den Df
Pr(>F)
# (Intercept)                  1     0.971    299.9      1      9
0.000000032 ***
# treatment                    2     0.492      4.4      2      9
0.04726 *
# gender                       1     0.193      2.1      1      9
0.17700
# age                          1     0.045      0.4      1      9
0.53351
# treatment:gender             2     0.389      2.9      2      9
0.10867
# phase                        1     0.855     23.6      2      8
0.00044 ***
# treatment:phase              2     0.696      2.4      4     18
0.08823 .
# gender:phase                 1     0.079      0.3      2      8
0.71944
# age:phase                    1     0.140      0.7      2      8
0.54603
# treatment:gender:phase       2     0.305      0.8      4     18
0.53450
# hour                         1     0.939     23.3      4      6
0.00085 ***
# treatment:hour               2     0.346      0.4      8     14
0.92192
# gender:hour                  1     0.286      0.6      4      6
0.67579
# age:hour                     1     0.262      0.5      4      6
0.71800
# treatment:gender:hour        2     0.539      0.6      8     14
0.72919
# phase:hour                   1     0.663      0.5      8      2
0.80707
# treatment:phase:hour         2     0.893      0.3     16      6
0.97400
# gender:phase:hour            1     0.700      0.6      8      2
0.76021
# age:phase:hour               1     0.813      1.1      8      2
0.56210
# treatment:gender:phase:hour  2     1.003      0.4     16      6
0.94434
# ---
# Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1


--
Dipl. Psych. Henrik Singmann
PhD Student
Albert-Ludwigs-Universit?t Freiburg
http://www.psychologie.uni-freiburg.de/Members/singmann

-- 
Dipl. Psych. Henrik Singmann
PhD Student
Albert-Ludwigs-Universit?t Freiburg
http://www.psychologie.uni-freiburg.de/Members/singmann