[R-sig-ME] constrain random effect in lmer (fitting reduced model for calculation of Cohen's f2)

[João Veríssimo]

Dear all,

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://d
oi.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.

1. Is there a way to achieve this in lmer(), i.e., to prespecify the
variance of a random effect?

2. If not: as a proxy for "holding the random effect constant" I've
assumed that the increased random effect variance in the reduced models
could be added to the residual variance.

For example, the random effect part of the "full" model shows 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 (which is the difference in the Subject effect when
said predictor is left out).

Are there objections to this? It seemed reasonable to me, but I'm not
sure at all.

Thank you!
João