[R-sig-ME] Fixed effects in lmer()

Thierry Onkelinx th|erry@onke||nx @end|ng |rom |nbo@be
Fri Jun 18 09:54:16 CEST 2021

Dear Duncan,

If the random effects only explain the noise of the linear regression, then
you could get similar fixed effect estimates. The summary of both models
would be useful.

IMHO R² has only a clear definition under very special conditions: a linear
regression with Gaussian distribution and without random effects.
Unfortunately, as people start learning statistics with this kind of model,
they assume that other models have the same properties. You could do an LRT
between models with and without the set of fixed effects.

Are you referring to non-negative random effects? The lmer random effects
assume a zero mean normal distribution. Which implies the possibility of
negative numbers.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey


Op vr 18 jun. 2021 om 08:24 schreef Duncan Jackson <duncanjackson using gmail.com

> Hi everyone.
> I have some questions about lmer() and I'm wondering if you might be able
> to help me out.
> I’ve run a mixed-model in lmer() including multiple random effects and a
> fixed effect.  I’ve noticed that if I run a comparison simple regression
> model with no random effects but the same fixed effect, I get precisely the
> same unstandardised beta coefficient for my fixed effect in the simple
> regression as I get if I run the mixed model.
> Am I correct in thinking, therefore, that the beta coefficients generated
> in the mixed model in lmer() do not control for the random effects in the
> model?  Would it make a difference in this respect if participants in my
> dataset were nested in a random effect?  Also, how does one summarise
> an overall R square value for the impact of a set of fixed effects in a
> mixed model with lmer()?
> On another note, I was wondering if there were any more recent suggestions
> about how to handle random effects in REML-based models using lmer() that
> are fenced at zero.  Is it possible that alternative optimizers might
> assist in this respect?  One issue I find when comparing lmer() with
> Bayesian estimators is that the difficulties in this respect often appear
> to arise with very small effects (i.e., those that approach near-zero
> variance estimates).
> Looking forward to hearing your thoughts.
> Kind regards,
> Duncan
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