[R-meta] Adding random effect to SCE models

[James Pustejovsky]

I see. To keep things organized, I'll offer some comments in the thread
that you linked above.

On Wed, Aug 4, 2021 at 11:34 AM Farzad Keyhan <f.keyhaniha using gmail.com> wrote:

> Hi James,
>
> Thank you for your informative response. I also appreciate Jack Solomon's
> helpful off-list comments (they may be helpful to other list members as
> well).
>
> To pick up on your last point which was that leaving the SCE's original
> random specification as is would imply that "true effect sizes at different
> time points are *fully* correlated if they come from the same study and the
> same category", one concern I have, as noted in my original email, is that
> most of my studies have multiple treatment groups in them.
>
> I realized that this issue has recently come up on the list (
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-July/003019.html).
> My collaborators have only "for indexing purposes" distinguished between
> treatment groups in each study (variable "grp").
>
> The post linked in the previous paragraph says: "it may be more
> "realistic" to assume that true effect sizes at different time points are
> correlated IF they come from the same treatment group in each study; rather
> than simply each study as a whole disregarding the groups."
>
> I agree (and perhaps you do too?) with that statement. In the case of my
> SCE model, my "time" random effect, then, has to change from: "~ time |
> interaction(study, mod_cat)" to now: "~ time | interaction(study, grp,
> mod_cat)". But as the follow-up answer (
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-July/003020.html)
> also explains, this strategy will produce a perhaps non-interpretable
> variance component for "grp".
>
> So, I was wondering what your thoughts are on using this strategy (i.e.,
> adding an indexing variable like "grp" in the random specification of
> "time")?
>
> All the best,
> Fred
>
> On Tue, Aug 3, 2021 at 10:24 PM James Pustejovsky <jepusto using gmail.com>
> wrote:
>
>> 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
>>
>> On Wed, Jul 21, 2021 at 3:42 PM Farzad Keyhan <f.keyhaniha using gmail.com>
>> wrote:
>>
>>> 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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>>>
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>>>
>>

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