Home › forums › Mixed Models › Why contr.sum for random effects grouping factors?
 This topic has 9 replies, 2 voices, and was last updated 1 year, 12 months ago by henrik.

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April 9, 2018 at 20:13 GMT+0000 #223statmerkurParticipant
It’s clear to me why one should use orthogonal contrast for categorical predictors in mixed models when one wants to estimate main effects (and interactions between them). But why does
mixed()
use contrast coding (i.e.contr.sum
) for the random effects grouping factors? This topic was modified 2 years ago by statmerkur.

April 9, 2018 at 20:31 GMT+0000 #225henrikKeymaster
mixed
simply usescontr.sum
for all categorical covariates per default. I agree that for the random effects that can lead to an awkward parameterization. However, it is not immediately clear to me how one could program it in a different way. So the reason is just convenience and having no apparent alternative. If you have very specific alternative ideas you can simply setcheck_contrasts = FALSE
and set the contrasts in the desired way. I honestly do not see the benefit of offering anything else via themixed
interface. But feel free to convince me otherwise. 
April 9, 2018 at 20:57 GMT+0000 #227statmerkurParticipant
I was just curious whether there was a specific reason for that. So, would you agree that using orthogonal contrasts for categorical covariates and, say, treatment coding for random effects grouping factors is equivalent to using orthogonal contrasts for both categorical covariates and random effects grouping factors?

April 10, 2018 at 07:57 GMT+0000 #228henrikKeymaster
No, I do not agree with that. To be honest, I do not fully understand where this purported equivalence should come from.
I agree that having randomslopes that have a sumtozero coding can lead to somewhat awkward parameterizations. Why should the deviations from the grandmean be normally distributed across participants? However, other coding schemes do not necessarily have better properties. So I am not sure what can be gained tby using different coding schemes for the fixedeffects and the randomslopes.
But maybe there is also a misunderstanding here. The coding for the randomeffects grouping factors is using dummycoding or what seems to be called onehot encoding in machine learning. Each level of the randomeffects grouping factor has its own parameter that is 1 for this level and 0 for all others. Thus, there is no intercept and random intercepts are simply estimated for each level individually.
Is this what you were after?

April 10, 2018 at 22:33 GMT+0000 #232statmerkurParticipant
There seems to be no difference between models with different coding schemes for the randomeffects grouping factors, i.e.
m1
=m2
andm3a
=m4a
. Hence I don’t understand whyafex
setscontr.sum
for the randomeffects grouping factors (Worker in the example below).Besides that, AFAIU,
m3b
andm4b
are models where random slopes are coded differently (treatment coding vs sum coding) and they seem to estimate the same random effects which in turn are the same asm5
s (which also suppresses the fixed intercept) estimates for the random effects.Why is that?
library(afex) data("Machines", package = "MEMSS") m1< mixed(score ~ Machine + (MachineWorker), Machines) contrasts(Machines$Machine) < contr.sum(length(levels(Machines$Machine))) m2 < mixed(score ~ Machine + (MachineWorker), Machines, check_contrasts = F) m1$full_model # Machine sum coded + Worker sum coded m2$full_model # Machine sum coded + Worker treatment coded contrasts(Machines$Machine) < contr.treatment(length(levels(Machines$Machine))) m3a < mixed(score ~ Machine + (MachineWorker), Machines, check_contrasts = F) m3b < mixed(score ~ Machine + (0 + MachineWorker), Machines, check_contrasts = F) contrasts(Machines$Worker) < contr.sum(length(levels(Machines$Worker))) m4a < mixed(score ~ Machine + (MachineWorker), Machines, check_contrasts = F) m4b < mixed(score ~ Machine + (0 + MachineWorker), Machines) m5 < mixed(score ~ 0 + Machine + (0 + MachineWorker), Machines, check_contrasts = F) m3a$full_model # Machine treatment coded + Worker treatment coded m4a$full_model # Machine treatment coded + Worker sum coded m3b$full_model # Machine treatment coded + Worker treatment coded + random intercept suppressed m4b$full_model # Machine sum coded + Worker sum coded + random intercept suppressed m5$full_model # Machine treatment coded + Worker sum coded + fixed and random intercept suppressed

April 11, 2018 at 21:01 GMT+0000 #234henrikKeymaster
What you observe and describe is of course the case (you bring the evidence), but is not directly related to
afex
but tolme4
andR
in general. But let me explain.First, what I have said in my last response holds for the randomeffects grouping factors. They will always be encoded with one parameter for each level. Thus, in the example the coding for
Worker
is irrelevant as long as you estimate random intercepts for it. Then,lme4
will always estimate one idiosyncratic random intercept for each level of worker. Hence the equivalence ofm1
andm2
.Second, suppressing the intercept for categorical covariates in
R
does something weird. It then estimates one parameter per level, but does not actually reduce the number of estimated parameters. See:ncol(model.matrix(~Machine, Machines)) # [1] 3 ncol(model.matrix(~0+Machine, Machines)) # [1] 3
This is different from the case with numerical covariates (note that the next code is statistically nonsensically):
ncol(model.matrix(~as.numeric(Machine), Machines)) # [1] 2 ncol(model.matrix(~0+as.numeric(Machine), Machines)) # [1] 1
So when you use
(0 + MachineWorker)
the coding scheme is again irrelevant because, again, one parameter is estimated per level.Hope that clears everything up.

April 11, 2018 at 21:38 GMT+0000 #235statmerkurParticipant
Thanks, that cleared things up for me.
What I still don’t understand is in which case the coding for the randomeffects grouping factors does make a difference. Can you please give an (R code) example for this situation? 
April 13, 2018 at 08:07 GMT+0000 #236henrikKeymaster
Hmm, I do not see a situation where it would matter. I repeat, they will always be encoded with one parameter per level (i.e., onehot encoding).

April 13, 2018 at 10:39 GMT+0000 #237statmerkurParticipant
OK, so
mixed
converts treatment coded random effects grouping factors to sum coded factors (viacontr.sum
) just by convention? 
April 14, 2018 at 18:42 GMT+0000 #238henrikKeymaster
Exactly.
mixed
transforms all categorical covariates that is part of the formula tocontr.sum
. I thought it might lead to bugs if I only do this selectively (e.g., try to detect what are the grouping variables).


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