[R-meta] Adding random effect to SCE models

[Farzad Keyhan]

For sure, much appreciated. I'll follow your comments in that thread, then.
Fred

On Wed, Aug 4, 2021 at 11:47 AM James Pustejovsky <jepusto using gmail.com> wrote:

> 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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