[R] new to repeated measures anova in R

Mon Mar 5 11:54:20 CET 2012

[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 Œ***‚ 0.001 Œ**‚ 0.01 Œ*‚ 0.05 Œ.‚ 0.1 Œ ‚ 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 Œ***‚ 0.001 Œ**‚ 0.01 Œ*‚ 0.05 Œ.‚ 0.1 Œ ‚ 1 
> 
>      HF eps Pr(>F[HF])    
> Shoe   0.92023     0.2008    
> Region 0.54302  5.227e-09 ***
> ---
> Signif. codes:  0 Œ***‚ 0.001 Œ**‚ 0.01 Œ*‚ 0.05 Œ.‚ 0.1 Œ ‚ 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 Œ***‚ 0.001 Œ**‚ 0.01 Œ*‚ 0.05 Œ.‚ 0.1 Œ ‚ 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]]
> 
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Peter Dalgaard, Professor
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