[R-meta] 3 candidate random structures

[Timothy MacKenzie]

Dear James,

Thank you, this is very helpful to know. Is there currently a way to
statistically test individual correlations between outcome levels (assuming
a "UN" structure, say in outcome | study, where the outcome has 3 levels)?

Also, do you think that struct="GEN" might also allow such correlations to
be investigated with more thoroughly? For example, if I specify my random
part as `random = ~ treat_length * outcome | study, struct = "GEN"` would
that allow understanding for how the correlations among outcome levels
change for various `treat_length`?

Also, in your hypothetical D specification, you suggested `~ outcome |
interaction(study,gr,time)` as one of the terms, that had me wondering why
you took `outcome` to be nested in `time` (I always thought the other way
around i.e., time being nested in outcome).

Kind regards,
Tim

On Sat, Aug 14, 2021 at 9:37 PM James Pustejovsky <jepusto using gmail.com> wrote:

> See responses below.
> Cheers,
> James
>
> On Fri, Aug 6, 2021 at 12:27 PM Timothy MacKenzie <fswfswt using gmail.com>
> wrote:
>
>> Dear James,
>>
>> I seem to have forgotten to answer your question at the start of your
>> answer. Yes, my outcomes are comparable across my studies. However, I have
>> no intention of generalizing beyond my outcome levels. This is because the
>> levels of my outcome correspond to a specific theory in my area of research
>> and can't be beyond what the theory describes.
>>
>
> This makes sense. In multivariate models like these, generalization is to
> a (hypothetical) population of the units on the right-hand side of the | in
> the random formula---that is, the units corresponding to the IDs---not to
> the levels of the outcomes. For instance, say that the outcome variable has
> levels A, B, C. If you use random = ~ outcome | study, then the model is
> describing the multivariate distribution of the outcomes (the joint
> distribution of A, B, C) in a population of studies, of which you have a
> sample. Some studies in the sample might report a only subset of outcomes
> (only A, or only A and B), but we could imagine that all of the outcomes
> *could* have been measured in every study.
>
>
>>
>> However, I want to take a somewhat multivariate approach and let my
>> outcome levels correlate with one another across my studies because I
>> actually want to investigate the interrelationships among the existing
>> levels of my outcome themselves.
>>
>> That's a good reason to use a multivariate model.
>
>
>> Given this context, can I ignore the generalizability aspect of the
>> multilevel/multivariate approach, and instead take this approach because it
>> allows for the correlation among the existing outcome levels to be
>> investigated?
>>
>>>
>>>>>
> Yes, I think so.
>

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