[R-sig-ME] specifying crossed random effects for glmmPQL / lme

[Van Rynald Liceralde]

Hello,

I'm trying to fit a GLMM on simulated response time data (continuous,
positively skewed) obtained from hypothetical participants (Subject)
responding to the same set of hypothetical items (Item), so it's a
fully-crossed design. I intend to include several crossed-random effects
for Subject and Item, so in lme4 language, it would look like the following:

glmer(y ~ x1*x2*z1 + (1+x1+x2|Subject) + (1|Item),
family=Gamma("identity"), data=foo)

However, as I read from Ben Bolker's GLMM FAQ (
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#fn1), the
estimation procedure used by glmer (adaptive Gauss-Hermite quadrature) can
only handle up to 2-3 random effects. Indeed, running glmer on my simulated
data not only results in inevitable non-convergence but also takes such a
long time to run.

Someone recommended to me to use MASS::glmmPQL instead because the cases in
which penalized quasi-likelihood (PQL) would perform poorly (count/binomial
DV, mean DV < 5) doesn't apply to my data (continuous DV, identity link,
many items, and many subjects). Moreover, PQL could handle more random
effects than GHQ; it could also allow for correlations of random effects to
be estimated; and it estimates the model faster than GHQ. (I don't actually
know about any of those being accurate characterizations of PQL and GHQ;
would be happy to be corrected and pointed to the right direction.)

The solution suggested online on CrossValidated is as follows:

> bar <- glmmPQL(y ~ x1*x2*z1, random=list(Subject=~1+x1+x2, Item=~1),
                 family=Gamma("identity"),data=foo)

but this way of doing it seems to model the random effect for Item as if it
was nested under Subject, but I want them to be identified as crossed. I
was wondering if someone can point me to how I'd be able to specify my
model using glmmPQL such that the effects of Subject and Item are truly
crossed. Thank you so much!

Sincerely,
Van Liceralde
-- 
Van Rynald T. Liceralde, BS, BA
Graduate Student, Cognitive Psychology
University of North Carolina at Chapel Hill

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