[R-sig-ME] Appropriate model reduction sequence for factorial design in glmmTMB

[Maarten Jung]

Hi Phillip,

Emi Tanaka`s slides look promising - thanks.
However, I`m still having a hard time mapping this to my example of a
2x3 within-subjects design.

Best,
Maarten

On Fri, Apr 3, 2020 at 11:53 PM Phillip Alday <phillip.alday using mpi.nl> wrote:
>
> Hi Maarten,
>
> It's been a while and I still haven't had the time to give your post the
> necessary thought to give you a proper answer ....
>
> That said, Dimitri Rizopoulos posted some course notes a while back
> (http://www.drizopoulos.com/courses/EMC/CE08.pdf). I found the
> presentation there quite nice in terms of thinking about symmetry and
> nesting structures. Emi Tanaka also has some great slides on "software
> design for linear mixed model specification" which I also found great
> for thinking about how these structures are represented in the syntax of
> various software.
>
> So I hope my non answer helps a bit ....
>
> Phillip
>
> On 22/10/19 10:01 pm, Maarten Jung wrote:
> > Dear list,
> >
> > Sorry for basically restating my question here [1], but I think it
> > might be worth a separate thread as it might well be much easier to
> > answer with glmmTMB.
> >
> > After going through the posts [2] and [3] again, I identified the
> > following nesting structure (arrows indicate nesting) as the one I
> > want to go with for modelling some new data:
> >
> > m1 -> m2a/m2b/m2c -> m3 -> m4
> >
> > #######################################################
> >
> > library("lme4")
> > data("Machines", package = "MEMSS")
> > d <- Machines
> > mat <- model.matrix(~ 0 + Machine, d)
> > A <- mat[, 1]
> > B <- mat[, 2]
> > C <- mat[, 3]
> >
> > m1 <- lmer(score ~ Machine + (0 + Machine | Worker), d)
> >
> > m2a <- lmer(score ~ Machine + (1 | Worker) + (0 + dummy(Machine, "A")
> > | Worker) +
> >
> >    (0 + dummy(Machine, "B") | Worker) +
> >
> >    (0 + dummy(Machine, "C") | Worker), d)
> >
> > m2b <- lmer(score ~ Machine + (1 | Worker) + (0 + A + B + C || Worker), d)
> >
> > m2c <- afex::lmer_alt(score ~ Machine + (1 | Worker) + (0 + Machine ||
> > Worker), d)
> >
> > # m2a, m2b, and m2c are equivalent
> > all.equal(logLik(m2a), logLik(m2b), logLik(m2c))
> >
> > m3 <- lmer(score ~ Machine + (1 | Worker) + (1 | Worker:Machine), d)
> >
> > m4 <- lmer(score ~ Machine + (1 | Worker), d)
> >
> > #######################################################
> >
> > In my new data there are multiple observations per cell of a (at
> > least) 2x3 within-subjects design.
> > I know that m1 (denoting the two factors with f1 and f2, respectively)
> > would look like
> >
> > lmer(y ~ f1*f2 + (1 + f1*f2 | subject), data)
> >
> > and I think like this in glmmTMB syntax
> >
> > glmmTMB(y ~ f1*f2 + us(f1*f2 | subject), data, REML = TRUE)
> >
> > So now I'm struggling to figure out what m2a (or m2b/m2c) and m3 would
> > look like in the (at least) 2-factorial case.
> > My guess is that m2 would look like this in glmmTMB syntax
> >
> > glmmTMB(y ~ f1*f2 + (1 | subject) + diag(0 + f1*f2 | subject), data,
> > REML = TRUE)
> >
> > and that this might correspond to the following afex:lmer_alt() model
> >
> > afex::lmer_alt(y ~ f1*f2 + (1 | subject) + (0 +  f1*f2 || subject ), data)
> >
> > But I'm not sure about m3.
> >
> > I would be grateful if someone could provide the appropriate glmmTMB
> > syntax (additionally or alternatively, lmer/afex::lmer_alt syntax is
> > still welcome in the other thread).
> >
> > Best,
> > Maarten
> >
> > [1] https://stat.ethz.ch/pipermail/r-sig-mixed-models/2019q4/028222.html
> > [2] https://stat.ethz.ch/pipermail/r-sig-mixed-models/2018q2/026775.html
> > [3] https://stats.stackexchange.com/questions/345842/what-is-the-appropriate-zero-correlation-parameter-model-for-factors-in-lmer
> >
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