Dropping correlations bet. random-effects in lme4 syntax
Please keep the list in CC. I would strongly advise against statistical testing of the correlation parameters. You can technically do a likelihood ratio test comparing models fit with | and with ||, because the zero-correlation models are a special case of the unrestricted-correlation model, but DO NOT DO THIS. The estimates of the correlation parameters are notoriously unstable: we typically don't have nearly enough data to estimate them (because you need both a large number of observations AND a large number of groups). Moreover, the correlation estimates are intertwined with the estimates of the variance parameters. The sampling distribution for the variance parameters often looks a lot like a mixture of a point-mass at zero and some other, bounded distribution. This results in the sampling distribution of the correlation parameter also having a point mass at ?1. We have an example of this in the MixedModels.jl docs (https://juliastats.org/MixedModels.jl/dev/bootstrap/); there is probably an lme4 equivalent somewhere on the internet. For a more practical take on what happens when leave out the correlation parameters, see e.g. this blog post by John Kruschke https://doingbayesiandataanalysis.blogspot.com/2019/07/shrinkage-in-hierarchical-models-random.html or this take on dropping correlations to simplify model structure but still do good inference by Reinhold Kliegl https://rpubs.com/Reinhold/22193 Phillip
On 4/10/20 9:33 am, Simon Harmel wrote:
Hi Phillip,
I need to ask one follow up question. Suppose I want to test only one
correlation in `m1`'s random-effects covariance matrix below (pick
anyone correlation you want) for its statistical significance. I assume
that I must use?a likelihood ratio test that?compares `m1` with a
"second model" in which that correlation is absent, right?
How would you specify that "second model" so you can perform?a
likelihood ratio test?
m1 <- lmer(y ~ A * B * C + (A * B * C ?| group), data = data)???
On Sat, Oct 3, 2020 at 1:54 PM Simon Harmel <sim.harmel at gmail.com
<mailto:sim.harmel at gmail.com>> wrote:
Awesome, thanks!?
On Sat, Oct 3, 2020 at 12:40 PM Phillip Alday <phillip.alday at mpi.nl
<mailto:phillip.alday at mpi.nl>> wrote:
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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