[R-sig-ME] lmer - individual slopes

[Ben Bolker]

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 experimental
> design 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? The
> individual slopes are extracted so that we can check whether the rate of
> learning 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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> 
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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.