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

[Maarten Jung]

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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