# Calculation of Cohen's f2 in mixed-effects regression (specifying random variance in reduced model)

I am attempting to calculate Cohen's f2 as a measure of "local" effect size in a mixed-effects regression model (Selya et al., 2012, https://doi.org/10.3389/fpsyg.2012.00111 ).

The procedure involves comparing 3 models in order to calculate the reduction in residual variance that can be attributed to the fixed effect of interest (the 3 models are a "full" model with all predictors, a reduced model without the fixed effect of interest, and a "null" model with no fixed effects; for specifics, see Eqs. 2 and 3 in Selya et al., 2012).

Importantly, it is necessary to obtain the variance of random effects from the "full" model and hold this constant (the random effect variance) when fitting the reduced models.

As I am doing this in lmer() in R and I suspect it is not possible to constrain the random effect variance to a known value, I've assumed that the increased random effect estimates in the reduced models could be added to the residual variance.

Specifically, the variances in the "full" model are Subject (Intercept)=0.264;Residual=0.532. Taking one predictor out, for which I want to calculate Cohen's f2, I get Subject (Intercept)=0.320; Residual=0.534. I have taken the residual variance of the reduced model to be 0.534+0.056 (the latter number is the difference in the Subject random effect when said predictor is left out).

Does this hold and can be assumed in mixed-effects regression?