[R-sig-ME] Interrupted time series on grouped data with count outcome in glmmTMB

[Sokolovsky, Alexander]

Hi all,

This is my first time sending a question to this list so apologies if I
miss something that is typically expected. I am trying to fit an
interrupted time series type model on grouped data (by individual).
Specifically, I am modeling compliance with a remote survey tool that
delivered 5 surveys a day for 28 days across two bursts. The outcome
variable is a count of missed surveys on days with any engagement (so range
0-4) (https://i.stack.imgur.com/FThRs.png). Ignoring covariates, the three
focal predictors are thus time (studyday_new), burst (wave), and time after
burst 2 starts (studyday_new_post). The model is specified as follows (and
I acknowledge I could be making a mistake here, I tried to follow Ben
Bolker's thoughts on fitting this models with temporal autocorrelation in
glmmTMB from
https://bbolker.github.io/mixedmodels-misc/notes/corr_braindump.html):

mod1_mde <- glmmTMB(missed_surveys ~ w1age + school + w1sex + w1hislat +
w1racer + studyday_new + wave + studyday_new_post + ar1(studyday_new_t +
0|id) + (1 |id), data = daily_data3_mde, family = "poisson")

This model converges. But when I plot the predicted values
(using ggpredict from ggeffects) over the observed daily means, the
predicted values appear to be underestimating the observed means.

Here is the plot: https://i.stack.imgur.com/bRfue.png

Now what's interesting to me is that when I fit this model to a gaussian
distribution instead, the resulting predicted values are reasonable:
https://i.stack.imgur.com/rIYnZ.png

And when I fit this model to a poisson distribution but exclude the AR
covariance structure and random intercept (both of which are obviously
critical) I also get reasonable predicted values:
https://i.stack.imgur.com/dWlho.png

(Please ignore the different labels on the plots I just copied the syntax
from other parts of my code when I was writing it).

So is there something I'm missing about getting predicted values from this
model?

All the best,
-- Alex

-- 
*Alexander W. Sokolovsky, PhD*
Assistant Professor
Center for Alcohol and Addiction Studies
Department of Behavioral and Social Sciences
E: Alexander_Sokolovsky using Brown.edu
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[image: Twitter]AlexSokoPhD <https://twitter.com/AlexSokoPhD>
“The greatest enemy of knowledge is not ignorance, it is the illusion of
knowledge.”
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