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Tamre Cardoso

2012-Mar-05 02:15 UTC

[R] new to repeated measures anova in R

Data set up as one observation/subject looks like (with a total of 10 subjects)
Two treatments: shoe type with 3 categories and region with 8 categories  ==>
24 "treatment" columns

Subject PHallux   PMidToes PLatToe   PMTH1  PMidMTH PLatMTH  PMidfoot  PRearfoot
LHallux  LMidToes LLatToe   LMTH1   LMidMTH LLatMTH LMidfoot  LRearfoot DHallux 
DMidToes DLatToe   DMTH1   DMidMTH DLatMTH DMidfoot DRearfoot
   1         203.230  169.970     75.090     208.420 168.860    129.150   
104.840   209.960    200.005  88.880      30.820     315.535 105.445    72.265  
88.195     211.280   198.970  113.525    65.640       237.175  148.790    86.105
69.830    222.230

R Code:

library(car)
pressure=read.csv("Shoe_data.csv",header=TRUE,sep=",")
datin.model=cbind(pressure[,2],pressure[,3],pressure[,4],pressure[,5],pressure[,6],pressure[,7],pressure[,8],pressure[,9],pressure[,10],pressure[,11],pressure[,12],pressure[,13],
 
pressure[,14],pressure[,15],pressure[,16],pressure[,17],pressure[,18],pressure[,19],pressure[,20],pressure[,21],pressure[,22],pressure[,23],pressure[,24],pressure[,25])
multmodel=lm(datin.model ~ 1)
Shoe <-
factor(c(rep("P",8),rep("L",8),rep("D",8)))
Region
<-factor(rep(c("Hallux","MidToes","LatToe","MTH1","MidMTH","LatMTH","MidFoot","Rearfoot"),3))
fact.idata <- data.frame(Shoe,Region)
pressure.aov = Anova(multmodel, idata=fact.idata, idesign = ~Shoe + Region,
type="III")
> summary(pressure.aov,multivariate=F)Univariate Type III Repeated-Measures ANOVA Assuming Sphericity

                 SS num Df Error SS den Df        F    Pr(>F)    
(Intercept) 6275173      1   192361      9 293.5961 3.535e-08 ***
Shoe           2340      2    11839     18   1.7786    0.1973    
Region       748644      7   299408     63  22.5037 6.181e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 


Mauchly Tests for Sphericity

       Test statistic  p-value
Shoe          0.72437 0.275329
Region        0.00032 0.006714


Greenhouse-Geisser and Huynh-Feldt Corrections
 for Departure from Sphericity

        GG eps Pr(>F[GG])    
Shoe   0.78393     0.2065    
Region 0.37482  8.391e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

        HF eps Pr(>F[HF])    
Shoe   0.92023     0.2008    
Region 0.54302  5.227e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Everything runs fine, except that Anova will not allow idesign = ~Shoe*Region

So to look for interaction I set up a long format data set with columns Subject,
Pressure, Shoe, Region--df now has 240 rows

Then I ran:

 pressure.alt.df=read.csv("ShoeDataAltFormat.csv",header=TRUE,sep=",")
 pressure.aovalt=aov(Pressure~(Shoe*Region)+Error(Subject/(Shoe*Region)),data=pressure.alt.df)
> summary(pressure.aovalt)
Error: Subject
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals  1 2346.6  2346.6               

Error: Subject:Shoe
     Df Sum Sq Mean Sq
Shoe  2   3248  1624.0

Error: Subject:Region
       Df Sum Sq Mean Sq
Region  7 606772   86682

Error: Subject:Shoe:Region
            Df Sum Sq Mean Sq
Shoe:Region 14  34345  2453.2

Error: Within
             Df Sum Sq Mean Sq F value    Pr(>F)    
Shoe          2     35    17.5  0.0063    0.9937    
Region        7 152734 21819.2  7.8272 2.469e-08 ***
Shoe:Region  14  15479  1105.6  0.3966    0.9747    
Residuals   192 535219  2787.6                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

QUESTIONS:  

1) Why does the Anova function not allow Shoe*Region?
2) Does the use of aov provide a correct test for Shoe:Region Interaction?
3) The main effect for Shoe from Anova has a denominator df=18; shouldn't
that correspond to one of the error terms from aov?
4) Is the Anova p-value of 0.1973 for the main effect of Shoe the correct test

Any help trying to understand exactly what is happening in Anova versus aov is
greatly appreciated.  Looking at interaction plots, there does not appear to be
a lot going on except for two regions with relatively (compared to other
regions) different means for at least one Shoe type within the Region.

Thank you,
Tamre
	[[alternative HTML version deleted]]

peter dalgaard

2012-Mar-05 10:54 UTC

head link

[R] new to repeated measures anova in R

[Apologies for duplicate. Forgot to Cc. the list 1st time around.]
On Mar 5, 2012, at 03:15 , Tamre Cardoso wrote:
> Data set up as one observation/subject looks like (with a total of 10
subjects)
> Two treatments: shoe type with 3 categories and region with 8 categories 
==> 24 "treatment" columns
> 
> Subject PHallux   PMidToes PLatToe   PMTH1  PMidMTH PLatMTH  PMidfoot 
PRearfoot LHallux  LMidToes LLatToe   LMTH1   LMidMTH LLatMTH LMidfoot 
LRearfoot DHallux  DMidToes DLatToe   DMTH1   DMidMTH DLatMTH DMidfoot DRearfoot
> 1         203.230  169.970     75.090     208.420 168.860    129.150   
104.840   209.960    200.005  88.880      30.820     315.535 105.445    72.265  
88.195     211.280   198.970  113.525    65.640       237.175  148.790    86.105
69.830    222.230
> 
> R Code:
> 
> library(car)
> pressure=read.csv("Shoe_data.csv",header=TRUE,sep=",")
>
datin.model=cbind(pressure[,2],pressure[,3],pressure[,4],pressure[,5],pressure[,6],pressure[,7],pressure[,8],pressure[,9],pressure[,10],pressure[,11],pressure[,12],pressure[,13],
> 
pressure[,14],pressure[,15],pressure[,16],pressure[,17],pressure[,18],pressure[,19],pressure[,20],pressure[,21],pressure[,22],pressure[,23],pressure[,24],pressure[,25])
> multmodel=lm(datin.model ~ 1)
> Shoe <-
factor(c(rep("P",8),rep("L",8),rep("D",8)))
> Region
<-factor(rep(c("Hallux","MidToes","LatToe","MTH1","MidMTH","LatMTH","MidFoot","Rearfoot"),3))
> fact.idata <- data.frame(Shoe,Region)
> pressure.aov = Anova(multmodel, idata=fact.idata, idesign = ~Shoe + Region,
type="III")
> 
>> summary(pressure.aov,multivariate=F)
> Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
> 
>               SS num Df Error SS den Df        F    Pr(>F)    
> (Intercept) 6275173      1   192361      9 293.5961 3.535e-08 ***
> Shoe           2340      2    11839     18   1.7786    0.1973    
> Region       748644      7   299408     63  22.5037 6.181e-15 ***
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 
> 
> 
> Mauchly Tests for Sphericity
> 
>     Test statistic  p-value
> Shoe          0.72437 0.275329
> Region        0.00032 0.006714
> 
> 
> Greenhouse-Geisser and Huynh-Feldt Corrections
> for Departure from Sphericity
> 
>      GG eps Pr(>F[GG])    
> Shoe   0.78393     0.2065    
> Region 0.37482  8.391e-07 ***
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 
> 
>      HF eps Pr(>F[HF])    
> Shoe   0.92023     0.2008    
> Region 0.54302  5.227e-09 ***
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 
> 
> Everything runs fine, except that Anova will not allow idesign =
~Shoe*Region
> 
> So to look for interaction I set up a long format data set with columns
Subject, Pressure, Shoe, Region--df now has 240 rows
> 
> Then I ran:
> 
>
pressure.alt.df=read.csv("ShoeDataAltFormat.csv",header=TRUE,sep=",")
>
pressure.aovalt=aov(Pressure~(Shoe*Region)+Error(Subject/(Shoe*Region)),data=pressure.alt.df)
> 
>> summary(pressure.aovalt)
> 
> Error: Subject
>        Df Sum Sq Mean Sq F value Pr(>F)
> Residuals  1 2346.6  2346.6               
> 
> Error: Subject:Shoe
>   Df Sum Sq Mean Sq
> Shoe  2   3248  1624.0
> 
> Error: Subject:Region
>     Df Sum Sq Mean Sq
> Region  7 606772   86682
> 
> Error: Subject:Shoe:Region
>          Df Sum Sq Mean Sq
> Shoe:Region 14  34345  2453.2
> 
> Error: Within
>           Df Sum Sq Mean Sq F value    Pr(>F)    
> Shoe          2     35    17.5  0.0063    0.9937    
> Region        7 152734 21819.2  7.8272 2.469e-08 ***
> Shoe:Region  14  15479  1105.6  0.3966    0.9747    
> Residuals   192 535219  2787.6                      
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 
> 
> QUESTIONS:  
> 
> 1) Why does the Anova function not allow Shoe*Region?
> 2) Does the use of aov provide a correct test for Shoe:Region Interaction?
> 3) The main effect for Shoe from Anova has a denominator df=18;
shouldn't that correspond to one of the error terms from aov?
> 4) Is the Anova p-value of 0.1973 for the main effect of Shoe the correct
test
> 
Notice that much of this comes from the "car" package, which has a
maintainer, who is the real expert on what is going on. Anyways

1) You're not saying what goes wrong, nor giving complete instructions for
reproduction, but I would kind of suspect that something is unhappy with having
a saturated design (0 df for within variation).

2) I think it would, sort of, if specified correctly. It's not giving you
the GG and HF corrections though.

3) It should, and aov() is not giving you any residuals except for "Error:
Within". Did you forget to make Subject a 10-level factor?

4) Assuming sphericity, yes, I think so; it compares the Shoe main effect to the
Shoe:Subject interaction. However, as you have the HF corrected value of 0.2008,
why not use it? For Region, that does seem to be of some importance since it
fails the sphericity test.

Notice that most of what Anova does can also be done with plain anova(), with a
little more legwork. Check ?anova.mlm for a very similar example to yours.

> Any help trying to understand exactly what is happening in Anova versus aov
is greatly appreciated.  Looking at interaction plots, there does not appear to
be a lot going on except for two regions with relatively (compared to other
regions) different means for at least one Shoe type within the Region.
> 
> Thank you,
> Tamre
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-- 
Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

John Fox

2012-Mar-05 13:45 UTC

head link

[R] new to repeated measures anova in R

Dear Tamre,

You didn't include your data, nor show the error produced with Anova() in
car by idesign = ~Shoe*Region. Your data appear to have the same structure
as the O'Brien-Kaiser example in ?Anova, but without the between-subject
design. I have no trouble producing a two-way within-subject ANOVA for the
O'Brien-Kaiser data, including the interaction:

---------- snip ----------
> 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)
> idata      phase hour
1   pretest    1
2   pretest    2
3   pretest    3
4   pretest    4
5   pretest    5
6  posttest    1
7  posttest    2
8  posttest    3
9  posttest    4
10 posttest    5
11 followup    1
12 followup    2
13 followup    3
14 followup    4
15 followup    5> 
> 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) ~  1, 
+              data=OBrienKaiser)
> summary(Anova(mod.ok, idata=idata, idesign=~phase*hour,
type="III"),multivariate=FALSE) 

Univariate Type III Repeated-Measures ANOVA Assuming Sphericity

                SS num Df Error SS den Df        F    Pr(>F)    
(Intercept) 7260.0      1   603.33     15 180.4972 9.100e-10 ***
phase        167.5      2   169.17     30  14.8522 3.286e-05 ***
hour         106.3      4    73.71     60  21.6309 4.360e-11 ***
phase:hour    11.1      8   122.92    120   1.3525    0.2245    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

. . .

---------- snip ----------

So what's the problem?

Best,
 John
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Tamre Cardoso
> Sent: March-04-12 9:15 PM
> To: r-help at r-project.org
> Subject: [R] new to repeated measures anova in R
> 
> Data set up as one observation/subject looks like (with a total of 10
> subjects) Two treatments: shoe type with 3 categories and region with 8
> categories  ==> 24 "treatment" columns
> 
> Subject PHallux   PMidToes PLatToe   PMTH1  PMidMTH PLatMTH  PMidfoot
> PRearfoot LHallux  LMidToes LLatToe   LMTH1   LMidMTH LLatMTH LMidfoot
> LRearfoot DHallux  DMidToes DLatToe   DMTH1   DMidMTH DLatMTH DMidfoot
> DRearfoot
>    1         203.230  169.970     75.090     208.420 168.860    129.150
> 104.840   209.960    200.005  88.880      30.820     315.535 105.445
> 72.265      88.195     211.280   198.970  113.525    65.640
> 237.175  148.790    86.105      69.830    222.230
> 
> R Code:
> 
> library(car)
> pressure=read.csv("Shoe_data.csv",header=TRUE,sep=",")
> datin.model=cbind(pressure[,2],pressure[,3],pressure[,4],pressure[,5],p
> ressure[,6],pressure[,7],pressure[,8],pressure[,9],pressure[,10],pressu
> re[,11],pressure[,12],pressure[,13],
> 
> 	pressure[,14],pressure[,15],pressure[,16],pressure[,17],pressure[,
> 18],pressure[,19],pressure[,20],pressure[,21],pressure[,22],pressure[,2
> 3],pressure[,24],pressure[,25])
> multmodel=lm(datin.model ~ 1)
> Shoe <-
factor(c(rep("P",8),rep("L",8),rep("D",8)))
> Region <-
>
factor(rep(c("Hallux","MidToes","LatToe","MTH1","MidMTH","LatMTH","MidF
> oot","Rearfoot"),3))
> fact.idata <- data.frame(Shoe,Region)
> pressure.aov = Anova(multmodel, idata=fact.idata, idesign = ~Shoe +
> Region, type="III")
> 
> > summary(pressure.aov,multivariate=F)
> Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
> 
>                  SS num Df Error SS den Df        F    Pr(>F)
> (Intercept) 6275173      1   192361      9 293.5961 3.535e-08 ***
> Shoe           2340      2    11839     18   1.7786    0.1973
> Region       748644      7   299408     63  22.5037 6.181e-15 ***
> ---
> Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
> 
> 
> Mauchly Tests for Sphericity
> 
>        Test statistic  p-value
> Shoe          0.72437 0.275329
> Region        0.00032 0.006714
> 
> 
> Greenhouse-Geisser and Huynh-Feldt Corrections  for Departure from
> Sphericity
> 
>         GG eps Pr(>F[GG])
> Shoe   0.78393     0.2065
> Region 0.37482  8.391e-07 ***
> ---
> Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
> 
>         HF eps Pr(>F[HF])
> Shoe   0.92023     0.2008
> Region 0.54302  5.227e-09 ***
> ---
> Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
> 
> Everything runs fine, except that Anova will not allow idesign >
~Shoe*Region
> 
> So to look for interaction I set up a long format data set with columns
> Subject, Pressure, Shoe, Region--df now has 240 rows
> 
> Then I ran:
> 
> 
pressure.alt.df=read.csv("ShoeDataAltFormat.csv",header=TRUE,sep=",")
> 
> pressure.aovalt=aov(Pressure~(Shoe*Region)+Error(Subject/(Shoe*Region))
> ,data=pressure.alt.df)
> 
> > summary(pressure.aovalt)
> 
> Error: Subject
>           Df Sum Sq Mean Sq F value Pr(>F)
> Residuals  1 2346.6  2346.6
> 
> Error: Subject:Shoe
>      Df Sum Sq Mean Sq
> Shoe  2   3248  1624.0
> 
> Error: Subject:Region
>        Df Sum Sq Mean Sq
> Region  7 606772   86682
> 
> Error: Subject:Shoe:Region
>             Df Sum Sq Mean Sq
> Shoe:Region 14  34345  2453.2
> 
> Error: Within
>              Df Sum Sq Mean Sq F value    Pr(>F)
> Shoe          2     35    17.5  0.0063    0.9937
> Region        7 152734 21819.2  7.8272 2.469e-08 ***
> Shoe:Region  14  15479  1105.6  0.3966    0.9747
> Residuals   192 535219  2787.6
> ---
> Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
> 
> QUESTIONS:
> 
> 1) Why does the Anova function not allow Shoe*Region?
> 2) Does the use of aov provide a correct test for Shoe:Region
> Interaction?
> 3) The main effect for Shoe from Anova has a denominator df=18;
> shouldn't that correspond to one of the error terms from aov?
> 4) Is the Anova p-value of 0.1973 for the main effect of Shoe the
> correct test
> 
> Any help trying to understand exactly what is happening in Anova versus
> aov is greatly appreciated.  Looking at interaction plots, there does
> not appear to be a lot going on except for two regions with relatively
> (compared to other regions) different means for at least one Shoe type
> within the Region.
> 
> Thank you,
> Tamre
> 	[[alternative HTML version deleted]]

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