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

[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-Universität Freiburg
> http://www.psychologie.uni-freiburg.de/Members/singmann
> 
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