[R-sig-ME] What is the appropriate zero-correlation parameter model for factors in lmer?
Maarten Jung
M@@rten@Jung @ending from m@ilbox@tu-dre@den@de
Tue May 22 11:00:37 CEST 2018
I see that fm2 is nested within fm3 and fm4.
But I have a hard time understanding fm3 and fm2 because, as Reinhold Kiegl
said, they specify the f:g interaction but without the g main effect. Can
someone provide an intuition for these models?
Also, it is not entirely clear to me what fm5 represents. It looks to me,
and again I am with Reinhold Kiegl , as if there were over-parameterization
going on.
Cheers,
Maarten
On Tue, May 22, 2018 at 9:45 AM, Reinhold Kliegl <reinhold.kliegl at gmail.com>
wrote:
> Ok, I figured out the answer to the question about fm2.
>
> fm2 is indeed a very nice baseline for fm3 and fm4. So I distinguish
> between min1LMM and min2LMM.
>
> fm1 = y ~ 1 + f + (1 | g) # minimal LMM version 1 (min1LMM)
> fm2 = y ~ 1 + f + (1 | f:g) # minimal LMM version 2 (min2LMM)
> fm3 = y ~ 1 + f + (0 + f || g) # zcpLMM with 0 in RE (zcpLMM_RE0)
> fm4 = y ~ 1 + f + (1 | g) + (1 | f:g) # LMM w/ f x g interaction
> (intLMM)
> fm5 = y ~ 1 + f + (1 | g) + (0 + f | g) # N/A
> fm6 = y ~ 1 + f + (1 + f | g) # maximal LMM (maxLMM)
> fm7 = y ~ 1 + f + (1 + f || g) # zcpLMM with 1 in RE (zcpLMM_RE1)
>
>
> (1) maxLMM_RE1 -> intLMM -> min1LMM # fm6 -> fm4 -> fm1
> (2) maxLMM_RE1 -> intLMM -> min2LMM # fm6 -> fm4 -> fm2
> (3) maxLMM_RE0 -> zcpLMM_RE0 -> min2LMM # fm6 -> fm3 -> fm2
> (4) maxLMM_RE1 -> zcpLMM_RE1 -> min1LMM # fm6 -> fm7 -> fm1 (new
> sequence)
>
>
> On Tue, May 22, 2018 at 12:21 AM, Reinhold Kliegl <
> reinhold.kliegl at gmail.com> wrote:
>
>> Sorry, I am somewhat late to this conversation. I am responding to this
>> thread, because it fits my comment very well, but it was initially
>> triggered by a previous thread, especially Rune Haubo's post here [1]. So I
>> hope it is ok to continue here.
>>
>> I have a few comments and questions. For details I refer to an RPub I put
>> up along with this post [2]. I start with a translation between Rune
>> Haubo's fm's and the terminology I use in the RPub:
>>
>> fm1 = y ~ 1 + f + (1 | g) # minimal LMM (minLMM)
>> fm3 = y ~ 1 + f + (0 + f || g) # zero-corr param LMM with 0 in RE
>> (zcpLMM_RE0)
>> fm4 = y ~ 1 + f + (1 | g) + (1|f:g) # LMM w/ fixed x random factor
>> interaction (intLMM),
>> fm6 = y ~ 1 + f + (1 + f | g) # maximal LMM (maxLMM)
>> fm7 = y ~ 1 + f + (1 + f || g) # zero-corr param LMM with 1 in RE
>> (zcpLMM_RE1)
>>
>> Notes: f is a fixed factor, g is a group (random) factor; fm1 to fm6 are
>> in Rune Haubo's post; fm7 is new (added by me). I have not used fm2 and fm5
>> so far (see below).
>>
>> (I) The post was triggered by the question whether intLMM is nested under
>> zcpLMM. I had included this LRT in my older RPub cited in the thread, but I
>> stand corrected and agree with Rune Haubo that intLMM is not nested under
>> zcpLMM. For example, in the new RPub, I show that slightly modified
>> Machines data exhibit smaller deviance for intLMM than zcpLMM despite an
>> additional model parameter in the latter. Thanks for the critical reading.
>>
>>
>> (II) Here are Runo Haubo's sequences (left, resorted) augmented with my
>> translation (right)
>>
>> (1) fm6 -> fm5 -> fm4 -> fm1 # maxLMM_RE1 -> fm5 -> intLMM -> minLMM
>> (2) fm6 -> fm5 -> fm4 -> fm2 # maxLMM_RE1 -> fm5 -> intLMM -> fm2
>> (3) fm6 -> fm5 -> fm3 -> fm2 # maxLMM_RE1 -> fm5 -> zcpLMM_RE0 -> fm2
>>
>> and here are sequences I came up with (left) augmented with translation
>> into RH's fm's.
>>
>> (1) maxLMM_RE1 -> intLMM -> minLMM # fm6 -> fm4 -> fm1
>> (3) maxLMM_RE0 -> zcpLMM_RE0 # fm6 -> fm3
>> (4) maxLMM_RE1 -> zcpLMM_RE1 -> minLMM # fm6 -> fm7 -> fm1 (new
>> sequence)
>>
>>
>> (III) I have questions about fm2 and fm5.
>> fm2: fm2 redefines the levels of the group factor (e.g., in the cake
>> data there are 45 groups in fm2 compared to 15 in the other models). Why is
>> fm2 nested under fm3 and fm6? Somehow it looks to me that you include an
>> f:g interaction without the g main effect (relative to fm4). This looks
>> like an interesting model; I would appreciate a bit more conceptual support
>> for its interpretation in the model hierarchy.
>> fm5: fm5 specifies 4 variance components (VCs), but the factor has
>> only 3 levels. So to me this looks like there is redundancy built into the
>> model. In support of this intuition, for the cake data, one of the VCs is
>> estimated with 0. However, in the Machine data the model was not
>> degenerate. So I am not sure. In other words, if the factor levels are A,
>> B, C, and the two contrasts are c1 and c2, I thought I can specify either
>> (1 + c1 + c2) or (0 + A + B + C). fm5 specifies (1 + A + B + C) which is
>> rank deficient in the fixed effect part, but not necessarily in the
>> random-effect term. What am I missing here?
>>
>> [1] https://stat.ethz.ch/pipermail/r-sig-mixed-models/2018q2/026775.html
>> [2] http://rpubs.com/Reinhold/391027
>>
>> Best,
>> Reinhold Kliegl
>>
>>
>> On Thu, May 17, 2018 at 12:43 PM, Maarten Jung <
>> Maarten.Jung at mailbox.tu-dresden.de> wrote:
>> >
>> > Dear list,
>> >
>> > When one wants to specify a lmer model including variance components
>> but no
>> > correlation parameters for categorical predictors (factors) afaik one
>> has
>> > to convert the factors to numeric covariates or use lme4::dummy(). Until
>> > recently I thought m2a (or equivalently m2b using the double-bar syntax)
>> > would be the correct way to specify such a zero-correlation parameter
>> model.
>> >
>> > But in this thread [1] Rune Haubo Bojesen Christensen pointed out that
>> this
>> > model does not make sense to him. Instead he suggests m3 as an
>> appropriate
>> > model.
>> > I think this is a *highly relevant difference* for everyone who uses
>> > factors in lmer and therefore I'm bringing up this issue again. But
>> maybe
>> > I'm mistaken and just don't get what is quite obvious for more
>> experienced
>> > mixed modelers.
>> > Please note that the question is on CrossValidated [2] but some
>> consider it
>> > as off-topic and I don't think there will be an answer any time soon.
>> >
>> > So here are my questions:
>> > How should one specify a lmm without correlation parameters for factors
>> and
>> > what are the differences between m2a and m3?
>> > Is there a preferred model for model comparison with m4 (this model is
>> also
>> > discussed here [3])?
>> >
>> > library("lme4")
>> > data("Machines", package = "MEMSS")
>> >
>> > d <- Machines
>> > contrasts(d$Machine) # default coding: contr.sum
>> >
>> > m1 <- lmer(score ~ Machine + (Machine | Worker), d)
>> >
>> > c1 <- model.matrix(m1)[, 2]
>> > c2 <- model.matrix(m1)[, 3]
>> > m2a <- lmer(score ~ Machine + (1 | Worker) + (0 + c1 | Worker) + (0 +
>> c2 |
>> > Worker), d)
>> > m2b <- lmer(score ~ Machine + (c1 + c2 || Worker), d)
>> > VarCorr(m2a)
>> > Groups Name Std.Dev.
>> > Worker (Intercept) 5.24354
>> > Worker.1 c1 2.58446
>> > Worker.2 c2 3.71504
>> > Residual 0.96256
>> >
>> > m3 <- lmer(score ~ Machine + (1 | Worker) + (0 + dummy(Machine, "A") |
>> > Worker) +
>> > (0 + dummy(Machine, "B") |
>> > Worker) +
>> > (0 + dummy(Machine, "C") |
>> > Worker), d)
>> > VarCorr(m3)
>> > Groups Name Std.Dev.
>> > Worker (Intercept) 3.78595
>> > Worker.1 dummy(Machine, "A") 1.94032
>> > Worker.2 dummy(Machine, "B") 5.87402
>> > Worker.3 dummy(Machine, "C") 2.84547
>> > Residual 0.96158
>> >
>> > m4 <- lmer(score ~ Machine + (1 | Worker) + (1 | Worker:Machine), d)
>> >
>> >
>> > [1] https://stat.ethz.ch/pipermail/r-sig-mixed-models/2018q2/
>> 026775.html
>> > [2] https://stats.stackexchange.com/q/345842/136579
>> > [3] https://stats.stackexchange.com/q/304374/136579
>> >
>> > Best regards,
>> > Maarten
>> >
>> > [[alternative HTML version deleted]]
>> >
>> > _______________________________________________
>> > R-sig-mixed-models at r-project.org mailing list
>> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>>
>
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