How to remake aov() to car package Anova() to get Mauchly's test for sphericity, Greenhouse-Geisser and eta-squared?

Question

I want to convert a code written for aov() to Anova() function in car-package.

anovadata3 <- within(anovadata3, {
  subject <- factor(subject)
  time <- factor(time)
  gender <- factor(gender)
  group <- factor(group)
  groupgender <- factor(groupgender)
})

anovadata3.aov <- aov(values ~ time*group*gender + Error(subject),
                      data = anovadata3)
summary(anovadata3.aov)

This code give the me the following output:

Error: subject
              Df Sum Sq Mean Sq F value  Pr(>F)   
group          1  32220   32220   8.632 0.00365 **
gender         1     30      30   0.008 0.92819   
group:gender   1     15      15   0.004 0.94952   
Residuals    221 824913    3733                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Error: Within
                   Df Sum Sq Mean Sq F value   Pr(>F)    
time                3  21160    7053   9.223 5.53e-06 ***
time:group          3  18338    6113   7.993 3.06e-05 ***
time:gender         3   1916     639   0.835  0.47486    
time:group:gender   3  11679    3893   5.091  0.00172 ** 
Residuals         663 507012     765                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

However when i try using the Anova() function from car-package i do:

library(car)
mlm <- lm(values ~ time*group*gender, data = anovadata3)
rfactor <- factor(c("time", "gender","group","groupgender","subject"))
anovadata3.aov <- Anova(mlm, idata = dataframe(rfactor), idesign = ~ rfactor, type ="III")
summary(anovadata3.aov)

Which gives me this output.

     Sum Sq                Df         F value              Pr(>F)       
 Min.   :     58.3   Min.   :  1   Min.   :  0.03871   Min.   :0.00000  
 1st Qu.:   1324.9   1st Qu.:  1   1st Qu.:  0.54230   1st Qu.:0.04997  
 Median :  10281.5   Median :  3   Median :  1.57697   Median :0.21357  
 Mean   : 196286.3   Mean   :100   Mean   : 34.03103   Mean   :0.31053  
 3rd Qu.:  12290.4   3rd Qu.:  3   3rd Qu.:  2.61758   3rd Qu.:0.50989  
 Max.   :1331924.5   Max.   :884   Max.   :262.67095   Max.   :0.84408  
                                   NA's   :1           NA's   :1  

Does anyone know how i can remake the code that i use for aov() to fit the Anova(). I tried to follow the tutorial from: https://gribblelab.wordpress.com/2009/03/09/repeated-measures-anova-using-r/

to try to get the Anova() correct. But it doesn't give an output that looks similar. I also see from the webpage that it's suppose so give Mauchlys and Greenhouse, which i don't get. Also does anyone know how to get the eta-squared in the anova results? Or is it necessary to use seperate function to calculate the eta (etaSquared()).

The data below was used for the test, and i'm trying to test if there is a significant difference in "values" between time, gender and group and interaction effects between the factors.

          values  testperiod subject gender group groupgender time
1   118.82660110     Pretest       1      2     2   BSTfemale    1
2    61.07615138     Pretest       2      2     2   BSTfemale    1
3    57.51022740     Pretest       3      2     2   BSTfemale    1
4    70.73637347     Pretest       4      2     2   BSTfemale    1
5     9.86907880     Pretest       5      2     2   BSTfemale    1
6    64.51579546     Pretest       6      2     2   BSTfemale    1
7    63.25669342     Pretest       7      2     2   BSTfemale    1
8   109.09354856     Pretest       8      2     2   BSTfemale    1
9   140.69340502     Pretest       9      2     2   BSTfemale    1
10   93.94269807     Pretest      10      2     2   BSTfemale    1
11   43.76802256     Pretest      11      2     2   BSTfemale    1

...
898  60.85271722 FU_12_month     223      1     2     BSTmale    4
899  82.75598576 FU_12_month     224      1     2     BSTmale    4
900 -32.38497309 FU_12_month     225      1     2     BSTmale    4

Answer 1

The question seems a bit vague as to what is desired, but it's certainly not the first time someone has had difficulty getting what they wanted out of R's multivariate functions. I'm hoping that the term eta-squared is satisfied by the section on "Multivariate Tests:" in the result from summary.Anova.mlm with multivariate=TRUE which returns Pillai, Wilks, Hotelling-Lawley, and Roy tests and then separate sections (regardless of the value of multivariate parameter) for "Mauchly Tests for Sphericity" and "Greenhouse-Geisser and Huynh-Feldt Corrections for Departure from Sphericity". I cannot tell if you just want the result scraped from a console session or if you wanted to do further processing with the results. (And that latter hope has occasioned more than one request on Rhelp in the past.)

The code on the help page for car::Anova can be used to build an example for further discussion if needed (since you did not include a data example that could be copied):

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
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, 
                data=OBrienKaiser)
class(AnoOBK <- Anova(mod.ok, idata= idata, idesign= ~phase*hour, type="III") # "Anova.mlm"

summary(AnoOBK)

> names(summary(AnoOBK))
[1] "type"               "repeated"           "multivariate.tests"
[4] "univariate.tests"   "pval.adjustments"   "sphericity.tests"  
[7] "SSPE"