Dropping correlations bet. random-effects in lme4 syntax
On 03/10/2020 19:24, Simon Harmel wrote:
Thanks for the additional information about the use of `0+` in the context of categorical variables:) So, by splitting the specification of the grouping variable like: lmer(y ~ A * B * C + (A * C | group) + (B|group) , data = data)??? I get the below correlation matrix. So, here we have created 2 different intercepts, one for each "split" of the same grouping variable, right?
Yes, by default R adds in an intercept. I recommend always writing 1+ or 0+ to make explicit what you want. (This was what I meant with "Note that life gets tricky with the interaction terms." in my first reply.)
I ask this because B has no correlation with the first split's (intercept) but it has a singular correlation with the second split's (intercept). The output looks confusing to a novice like me. ? ? ? ? ? ? (Intercept) ? ? ?A ? ? ?C ? ?A:C (Intercept) ?B (Intercept) ? ? ? 1.000 -0.794 -0.195 ?0.953 ? ? ? ? ? 0 ?0 A ? ? ? ? ? ? ? ?-0.794 ?1.000 ?0.278 -0.854 ? ? ? ? ? 0 ?0 C ? ? ? ? ? ? ? ?-0.195 ?0.278 ?1.000 ?0.028 ? ? ? ? ? 0 ?0 A:C ? ? ? ? ? ? ? 0.953 -0.854 ?0.028 ?1.000 ? ? ? ? ? 0 ?0 (Intercept) ? ? ? 0.000 ?0.000 ?0.000 ?0.000 ? ? ? ? ? 1 -1 B ? ? ? ? ? ? ? ? 0.000 ?0.000 ?0.000 ?0.000 ? ? ? ? ?-1 ?1
Singularity isn't a problem per se -- it's mathematically well defined and being able to fit singular covariance matrices for the random effects was one of the algorithmic innovations lme4 has compared to its predecessor nlme. Singularity can be a problem for inference (because it's often a sign of overfitting).... but it makes sense here. B has no correlation with the first intercept because you set it to be zero via your formula specification, so that term is forced to be zero in the model computation. The second intercept is perfectly correlated with B because it (the second intercept) is redundant in the model, but it can't correlate with the first intercept (because that correlation is forced to zero by your model specification) and so it collapses into B. If B is continuous, you can avoid this with 0+B. If B is categorical, then 0+B will still be overparameterized, but you can try 0+dummy(B) to set up indicator variable for one of the two levels. (I can tell from your output that B is continuous or only has two levels because there is only one slope for it.) Phillip
On Sat, Oct 3, 2020 at 11:52 AM Phillip Alday <phillip.alday at mpi.nl
<mailto:phillip.alday at mpi.nl>> wrote:
I have no idea what 0* means, but 0+ means "suppress the
intercept" (which has knock-on effects for categorical variables
and whether they're represented in the model as (nlevels-1)
contrasts or nlevels).
For the other things: try it out. The output of summary(m1) will
show you which levels and correlations were kept.
On 03/10/2020 18:44, Simon Harmel wrote:
Thanks Phillip. What would be the meaning of placing `0 +` next
to any of the random effects (e.g., B) as shown in m2?
m1 <- lmer(y ~ A * B * C + (A * C | group) + (B|group) , data =
data)??
m2 <- lmer(y ~ A * B * C + (A * 0+ B * C ?| group), data = data)??
On Sat, Oct 3, 2020 at 11:33 AM Phillip Alday
<phillip.alday at mpi.nl <mailto:phillip.alday at mpi.nl>> wrote:
You can split the specification of your grouping to achieve
this, at
least in part:
lmer(y ~ A * B * C + (A * C | group) + (B|group) , data = data)
Note that life gets tricky with the interaction terms.
Phillip
On 03/10/2020 06:35, Simon Harmel wrote:
> Hello all,
>
> I know to drop all correlations among all level-1
predictors in the random
> part of an lmer() call, I can use `||`. But I was wondering
how to drop
> correlations (a) "individually" or (b) "in pairs"?
>
> Example of (a) is how to drop the correlation of B with
others (A & C)?
> Example of (b) is how to drop the correlation between B and C?
>
> lmer(y ~ A * B * C + (A * B * C? || group), data = data)
>
> Thanks,
> Simon
>
>? ? ? ?[[alternative HTML version deleted]]
>
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