[R-meta] 3 candidate random structures

James Pustejovsky jepu@to @end|ng |rom gm@||@com
Sun Aug 15 04:37:18 CEST 2021

See responses below.

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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