[R-meta] Adding random effect to SCE models

Hi Farzad,

It's definitely possible to add further levels of random effects within
each subgroup. (We didn't give examples of this in the paper due to space
constraints.)

I think the specification that you wrote in your original email could work
with variety of different structures for the second set of random effects.
For instance, struct = "CS" would imply a simple random effect for each
study-category combination, struct = "HCS" would allow differing variance
by time-point, or struct = "AR" would allow for an auto-regressive
structure per time-point. The one drawback of these specifications is that
the variance of the random effects is assumed to be constant across
moderator categories. That might or might not be reasonable--it's a
question of empirical fit.

Alternately, you could try something along the lines of
random = list(~ mod_cat | study, ~ mod_cat | interaction(study,time)),
struct = c("DIAG","DIAG")
which will give you a time-point specific random effect with a unique
variance component for every level of mod_cat.

Alternately, you could just leave it as the SCE model. You wrote: "we want
to encode the assumption that the true effect sizes at different time
points are correlated if they come from the study and the same category."
The regular SCE model (using random = ~ mod_cat | study, struct = "DIAG")
already encodes that assumption. It implies that true effect sizes at
different time points are *fully* correlated if they come from the same
study and the same category, due to there being just one random effect per
study-category.

Kind Regards,
James

Dear James (and the List Member),

First of all, what a useful paper (congrats!). My colleagues and I want to
fit separate SCE models to a number of categorical moderators in our
longitudinal studies (data structure is below, note that multiple rows with
the same time indicator are due to multiple treatment groups in each study,
not any additional outcome measures).

In your paper, although you talk about adding random effects per data
particulars, you seem to mainly mean that for your CHE model.

In our SCE models, we want to encode the assumption that the true effect
sizes at different time points are correlated if they come from the study
and the same category (*a bit unsure whether being from the same category
is quite needed*).

(1) Does this assumption make sense given the purpose of the SCE model
that you had in mind?
(2) If yes, what choices of "struct=" would make sense (to be empirically
confirmed)?

** mods = ~ mod_cat*time, random = list(~ mod_cat | study, ~ time |
interaction(study,mod_cat)), struct = c("DIAG","???") **

study mod_cat time
1       1             0
1       2             0
1       1             1
1       2             1
2       1             0
2       2             1
3       1             0

Thanks,
Fred

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