I now have a problem with effect size of LMM. Someone insisted that I should have effect sizes after p values. I then thought that I can use 'estimate' in the output of pairwise comparison using lsmeans function. He is not convinced by using estimate and suggested me to use cohen's d. Then I look at the calculation of cohen'd; it only uses means and SD of groups; it does not come from variance in LMM.
Another thing is also about effect size, I have used mixed function in afex in R which gives me overall significant values of parameters, but does not provide me effect size. Then I emailed asking the author of that function how I can have effect size, and he replied that there is no agreement on how to calculate effect size in LMM, so he didn't provide in that function, but again my colleague insisted that I should have it. I feel like if I have to us effect size calculated from ANOVA table, then it is not effect size of LMM that I calculate. This is output from LMM in afex.
> mixed3 <- mixed(peak_Mid ~ (1|item) + (1+vowel3|speaker) + sex*vowel3*Language, data=data1.frame, na.action=na.omit)
Fitting 9 (g)lmer() models:
[.........]
Obtaining 8 p-values:
[Note: method with signature ‘sparseMatrix#ANY’ chosen for function ‘kronecker’,
target signature ‘dgCMatrix#ngCMatrix’.
"ANY#sparseMatrix" would also be valid
........]
> summary(mixed3)
Effect stat ndf ddf F.scaling p.value stat.U ndf.U ddf.U F.scaling.U p.value.U
1 (Intercept) 9500.922104 1 70.40672 1.0000000 7.529698e-77 9500.922104 1 70.40672 NA 7.529698e-77
2 sex 15.980281 1 71.52842 1.0000000 1.538529e-04 15.980281 1 71.52842 NA 1.538529e-04
3 vowel3 8.596702 2 27.40531 0.9916348 1.264905e-03 8.669222 2 27.40531 NA 1.209863e-03
4 Language 3.996819 2 70.74337 0.9909675 2.267036e-02 4.033250 2 70.74337 NA 2.194066e-02
5 sex:vowel3 1.746398 2 75.92257 0.9870432 1.813334e-01 1.769323 2 75.92257 NA 1.774036e-01
6 sex:Language 4.136050 2 170.78334 0.9964821 1.761500e-02 4.150652 2 170.78334 NA 1.737140e-02
7 vowel3:Language 1.573332 4 66.15951 0.9799283 1.917146e-01 1.605559 4 66.15951 NA 1.832701e-01
8 sex:vowel3:Language 1.239002 4 195.29430 0.9894859 2.956981e-01 1.252168 4 195.29430 NA 2.903144e-01
>
Do you have any suggestions on if LMM has any way to calculate effect size rather than using estimate?