[R-sig-ME] lmer - individual slopes

[ji@verissimo m@iii@g oii gm@ii@com]

Hi Cátia,

To follow-up on Ben's answer,

Note that in the model Ben suggested (with the interaction), the by-
Participant random effects for Congruency will be deviations relative
to the mean Congruency effect in each group, I believe.
So similar random-effect adjustments (from ranef) for participants in
different groups may actually correspond to different predicted
individual slopes, depending on the effect of Congruency in each group.

In contrast, in your models (both a and b, I think), the by-Participant 
random effects for Congruency will be deviations from the mean
Congruency effect estimated across all participants.
(the two models would differ in the interpretation of their random
intercept adjustments, though)

João

On Wed, 2022-01-05 at 20:23 -0500, Ben Bolker wrote:
> On 1/5/22 8:10 PM, Cátia Ferreira De Oliveira via R-sig-mixed-models
> wrote:
> > Hello,
> > I hope you had a lovely winter break.I am interested in extracting
> > the individual slopes for an experimentaldesign where individuals
> > are asked to do a task with two conditions -congruent and
> > incongruent. These participants are also divided into groups- sleep
> > or awake. Should I consider group allocation in the model?
> > Theindividual slopes are extracted so that we can check whether the
> > rate oflearning is stable across sessions.Should we use:
> > a) lmer(Response times ~ Congruency + Group + (Congruency|
> > Participant)
> > Or is it ok to just have it as:
> > b) lmer(Response times ~ Congruency + (Congruency| Participant)
> > Thanks
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> > 
> 
>    I don't see why you wouldn't use Congruency*Group as your fixed
> effect?  The more accurately you can estimate the population-level
> effects in the fixed-effect part of the model, the less is left for
> the random effects component to explain, which in turn makes it more
> likely that the distribution will conform to the assumption of
> normality.
>    For example, suppose (retreating from a random-slopes model to a
> random-intercept model) that you had a treatment, ttt, with two
> levels and  a large effect, with subjects allocated to one treatment
> or the other (a nested design).  If you fitted
>    lmer(response ~ 1 + (1|subject)
> the distribution of subject-level effects would be strongly bimodal,
> since it would have to account for the treatment effect as well,
> whereas
>    lmer(response ~ ttt + (1|subject)
> would move the signal into the fixed effect and allow the random
> effect to capture the smaller (and possibly Normal) subject-level
> effects.
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