Removing random intercepts before random slopes

On Wed, Aug 29, 2018 at 12:41 PM Phillip Alday <phillip.alday at 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