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

Henrik Singmann henrik.singmann at psychologie.uni-freiburg.de
Sun Jul 22 22:06:58 CEST 2012

```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
> 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
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
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>> guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
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