[R] Sphericity for a repeated measure ANOVA with whithin and between subjects design, using R

[angelo.arcadi at virgilio.it]

 Dear List Members,



I need to perform a four-way ANOVA with repeated measures and to 
calculate the sphericity for eventual correction of the degree of 
freedom of the F ratio.
I have three within subjects factors (Emotion, having 5 levels, 
Material, having 4 levels, Shoes, having 2 levels) and a between subject
 factor (Musician, having 2 levels). Without considering the sphericity I
 use the following formula

aov_SPL = aov(SPL ~ Emotion*Material*Shoes*Musician + Error(Subject/(Emotion*Material*Shoes)), data=scrd)



Unfortunately after having read lot of material online I did not 
arrive to a solution about how to calculate for my case the epsilon of 
the Greenhouse-Geisser method for degree of freedom adjustment.


I load my data in R with this formula:

scrd<- read.csv(file='/path to data/data.csv',sep=',',header=T)



and this is the structure of the imported table:

> head(scrd)
    Subject Material       Shoes    Emotion  H2H H2H_factor SPL_factor SPL_variation     SPL Musician Weight Height
1  Subject1   Gravel dress_shoes AGGRESSIVE  468      0.736     11.591        21.283  97.383       no     90    183
2  Subject1   Gravel dress_shoes      HAPPY  719      1.129      3.188        10.071  86.171       no     90    183
3  Subject1   Gravel dress_shoes     TENDER 1129      1.774      5.114        14.176  90.276       no     90    183
4  Subject1   Gravel dress_shoes        SAD 1010      1.587     13.102        22.347  98.447       no     90    183
5  Subject1   Gravel dress_shoes    NEUTRAL  736      1.156      3.161         9.995  86.095       no     90    183
6 Subject10   Gravel dress_shoes AGGRESSIVE  635      0.998     15.849        24.000 100.100      yes     70    178
> 



I noticed that in the car package there is the Anova() function that 
comes with the Maulchy's sphericity test, but it does not take as an 
input a model generated with aov(). I need to use lm() instead, but 
since
I am not really proficient in R I do not know how to use the lm() 
starting from the loaded data and how to use Anova(). In addition, being
 a mixed design involving within and between subjects factors I wonder 
if Anova() is the most appropriate function to use for my case.


Is there anyone who could provide me with the R code to calculate the
 Maulchy's test and the epsilon of Greenhouse-Geisser for my case?


Thank you in advance
Best

Angelo


       
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