eta-squared in lmer

Actually, the ez package provides estimates of generalized eta-squared
for ANOVA only, sorry. That said, it could be argued that measures of
effect size (like eta-squared) represent a half-hearted attempt by
scientists to move beyond the impoverished information provided by
p-values, and that a full-hearted alternative that provides the
information we really want as scientists is the likelihood ratio. To
this end, ez *does* provide likelihood ratios for fixed effects in
mixed effects models with simple random effects structures (eg. no
"varying slopes" models).

Hello ALL!
Until now I have never been asked to provide (partial) eta-squared for any
of my lmer models. However, reviewers in a journal where I plan to submit
have strict policy of having this particular statistics. I know about EZ
package, and that it could/should do something of the kind, but I do not
know details. Please, can anyone tell me how can I get etas from typical
lmer model? I know general logic of it, but never dig deeper. Moreover, I
think I've read somewhere that it is biased. Can you suggest some good
reference?

Thanks,
PM

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