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

[peter dalgaard]

Another method goes via anova.mlm(), which is pretty straight forward once you figure out how to set up the necessary within-subject projections (contrasts). See

@Article{Rnews:Dalgaard:2007,
 author       = {Peter Dalgaard},
 title        = {New Functions for Multivariate Analysis},
 journal      = {R News},
 year         = 2007,
 volume       = 7,
 number       = 2,
 pages        = {2--7},
}

and ?anova.mlm.

-pd

> On 06 Jul 2015, at 18:17 , John Fox <jfox at mcmaster.ca> wrote:
> 
> Dear Angelo,
> 
> One way to do this is with the Anova() function in the car package; see the
> following article in the R Journal:
> 
> @Article{RJournal:2013-1:fox-friendly-weisberg,
> author       = {John Fox and Michael Friendly and Sanford Weisberg}, 
> title        = {Hypothesis Tests for Multivariate Linear Models Using the
> {car} Package}, 
> journal      = {The R Journal},
> year         = 2013,
> volume       = 5,
> number       = 1,
> pages        = {39--53},
> month        = jun,
> url          =
> {http://journal.r-project.org/archive/2013-1/RJournal_2013-1_fox-friendly-we
> isberg.pdf}
> 
> I hope this helps,
> John
> 
> 
> -----------------------------------------------
> John Fox, Professor
> McMaster University
> Hamilton, Ontario, Canada
> http://socserv.socsci.mcmaster.ca/jfox/
> 
> 
> 
>> -----Original Message-----
>> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of
>> angelo.arcadi at virgilio.it
>> Sent: July-06-15 10:05 AM
>> To: r-help at r-project.org
>> Subject: [R] Sphericity for a repeated measure ANOVA with whithin and
>> between subjects design, using R
>> 
>> 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
>> 
>> 
>> 
>> 	[[alternative HTML version deleted]]
>> 
>> ______________________________________________
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>> guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> 
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> ______________________________________________
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-- 
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