[R-sig-ME] Removing random intercepts before random slopes

[Maarten Jung]

Sorry, hit the send button too fast:

# here  c1 and c2 represent the two contrasts/numeric covariates defined
for the three levels of a categorical predictor
m1 <- y ~ 1 + c1 + c2 + (1 + c1 + c2 || group)

On Wed, Aug 29, 2018 at 2:07 PM Maarten Jung <
Maarten.Jung using mailbox.tu-dresden.de> wrote:

>
> On Wed, Aug 29, 2018 at 12:41 PM Phillip Alday <phillip.alday using mpi.nl>
> wrote:
> >
> > Focusing on just the last part of your question:
> >
> > > And, is there any difference between LMMs with categorical and LMMs
> > > with continuous predictors regarding this?
> >
> > Absolutely! Consider the trivial case of only one categorical predictor
> > with dummy coding and no continuous predictors in a fixed-effect model.
> >
> > Then ~ 0 + cat.pred  and ~ 1 + cat.pred produce identical models in some
> > sense, but in the former each level of the predictor is estimated as an
> > "absolute" value, while in the latter, one predictor is coded as the
> > intercept and estimated as an "absolute" value, while the other levels
> > are coded as offsets from that value.
> >
> > For a really interesting example, try this:
> >
> > data(Oats,package="nlme")
> > summary(lm(yield ~ 1 + Variety,Oats))
> > summary(lm(yield ~ 0 + Variety,Oats))
> >
> > Note that the residual error is identical, but all of the summary
> > statistics -- R2, F -- are different.
>
> Sorry, I just realized that I didn't make clear what I was talking about.
> I know that  ~ 0 + cat.pred and ~ 1 + cat.pred in the fixed effects part
> are just reparameterizations of the same model.
> As I'm working with afex::lmer_alt() which converts categorical
> predictors to numeric covariates (via model.matrix()) per default, I was
> talking about removing random intercepts before removing random slopes in
> such a model, especially one without correlation parameters [e.g. m1],
> and whether this is conceptually different from removing random
> intercepts before removing random slopes in a LMM with continuous
> predictors.
> I. e., I would like to know if it makes sense in this case vs. doesn't
> make sense in this case but does for continuous predictors vs. does never
> make sense.
>
> # here  c1 and c2 represent the two contrasts/numeric covariates defined
> for the three levels of a categorical predictor
> m1 <- y ~ 1 + c1 + c2 + (1 + c1 + c2 ||  cat.pred)
>
> Best,
> Maarten
>

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