Appropriate model reduction sequence for factorial design in glmmTMB

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