[R-meta] 3 candidate random structures

[Jack Solomon]

Dear Tim,

To your second question (using struct="GEN"), I believe at least `random =
~ treat_length + outcome | study, struct = "GEN"` (using `treat_length` as
a control variable) is supported by rma.mv.

You can also then turn your correlation estimates (note
that struct="GEN" considers a semi-definite positive structure for the
var-covar matrix of random slopes and intercepts, kind of "UN"ish) into
regression coefficients in which case you essentially can perform a latent
regression (i.e., regression on random effects using any one of them as DV
and one or more of them as IVs).

I'm a bit new to rma.mv and I'm still exploring it myself, but given that
the behavior of random effects under struct="GEN" is apparently similar to
the conventional multilevel models, such a regression can be performed
perhaps using something along the lines of:
https://github.com/rnorouzian/e/blob/master/e.r#L264 .

Then, you can probably also perform statistical significance on the
resultant regression coefficients using some form of bootstrapping like:
https://github.com/rnorouzian/e/blob/master/e.r#L303 .

Generally, such structures help bringing continuous variables more into the
discussion of multilevel meta-regression models which IMHO offers more
opportunities to ask and answer novel questions in meta-analysis. The
trouble, though, as always, is the size of the data needed to support such
models.

Definitely, Wolfgang has more to say about this, as struct="GEN" is as of
yet not documented.

Just my two cents,
Jack

On Mon, Aug 16, 2021 at 9:44 AM James Pustejovsky <jepusto using gmail.com> wrote:

> Responses below.
>
> James
>
> On Sat, Aug 14, 2021 at 10:28 PM Timothy MacKenzie <fswfswt using gmail.com>
> wrote:
>
> > 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)?
> >
>
> Yes. This can be tested using a likelihood ratio test comparing the full
> model to a model with one (or more) of the correlations fixed to specified
> values. You can fix these values using the rho argument in rma.mv. See the
> section "Fixing Variance Components and/or Correlations" of ?rma.mv.
>
>
> >
> > 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`?
> >
> >
> Does that syntax even work? I'm not sure how you would interpret it.
>
>
> > 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).
> >
> >
> Either way (outcomes nested in timepoints or timepoints nested in outcomes)
> entails some simplifying assumptions. It seems more plausible that there
> would be some structured correlation between all of the effect sizes within
> a given study (including correlation between effects from different
> outcomes at different time points) but I don't think it's possible to fit
> something like that with rma.mv().
>
>
> > 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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