Obtaining Effect Sizes from Linear Mixed Model (lme4)

Question

Say I want to obtain some sort of effect size for each term in a lmer object, what's the best way to do this? For example, I have this model with two main effects ( gen and nutrient ) and their interaction:

library(lme4)
data(Arabidopsis)
fit1 <- lmer(total.fruits~gen*nutrient+(1|reg), data=Arabidopsis)
summary(fit1)

# # # truncated output

Random effects:
 Groups   Name        Variance Std.Dev.
 reg      (Intercept)  144.4   12.02   
 Residual             1304.4   36.12   
Number of obs: 625, groups:  reg, 3

Fixed effects:
              Estimate Std. Error        df t value Pr(>|t|)    
(Intercept)    4.35938   10.72391   7.20000   0.407    0.696    
gen            0.13441    0.39560  67.90000   0.340    0.735    
nutrient       6.62369    0.99266 619.40000   6.673 5.58e-11 ***
gen:nutrient  -0.09971    0.04308 619.50000  -2.314    0.021 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

If I wanted to get an effect size (R2 or pseudo-R2) for each fixed effect main effect and the interaction term, what is the best approach to doing this? Obtaining the R2 for a full model (a la MuMIn::r.squaredGLMM(fit1) ), and use a model comparison approach as I build up to the final model? Or is there a better way?

Answer 1

Did you try the sem.model.fits function from this packages https://cran.r-project.org/web/packages/piecewiseSEM/piecewiseSEM.pdf ? You should be able to obtain pseud R2 for both varying and fixed effects. If you want effect sizes corresponding to specific parameters instead of the entire model, you can decompose the models with fewer parameters and work with model comparison.

Answer 2

Effect sizes for metric data can be calculated with r = √(t²/(t^2+df)) (Rosenthal, 1991, p. 19) r<-sqrt(t^2/(t^2+df)) for the fixed facotr gen: sqrt(0.340^2/(0.340^2+68)) #0,04, which means no effect Intepretation according to Cohen (1992). I know, that there is a reference of Cohen, which i more often cited (Cohen 1988), however the 1992 reference is the one, I read:

lower 0.1: no effect 0.1-0.29: small effect 0.3-0.49: medium effect 0.5-1: large effect

Rosenthal, R. 1991. Meta-analytic Procedures for Social Research. 2nd ed., Sage Publications, Newbury Park. Cohen J 1992 A power primer. Psychological Bulletin 112: 155-159.