[R-meta] mean-variance relationships introduces additional heterogeneity, how?

[James Pustejovsky]

All I mean is that a skewed distribution or one with large outliers
does not necessarily *imply* that a mean-sd relationship exists. It
could be the result of one, but skewness might be due to something
else (such as selective reporting) instead.

I would suggest that a well-behaved effect distribution is desirable
and appropriate to the extent that it indicates empirical regularity
of the phenomenon you're interested in. A less heterogeneous
distribution means that effects are more predictable (at least in the
corpus of studies that you're examining).

On Mon, Oct 25, 2021 at 8:58 PM Luke Martinez <martinezlukerm using gmail.com> wrote:
>
> I thought the existence of outlying effect estimates under SMD and
> lack of it under LRR could attest to the existence of
> heterogeneity-generating artefacts like mean-sd relationships (and/or
> variation in measurement error) across the studies.
>
> If not, then, would you mind commenting on why a more symmetric and
> well-behaved effect distribution is equated with its appropriateness
> for a set of summaries (e.g., means & sds) from studies?
>
> Luke
>
> On Mon, Oct 25, 2021 at 8:47 PM James Pustejovsky <jepusto using gmail.com> wrote:
> >
> > Responses below.
> >
> > On Mon, Oct 25, 2021 at 4:21 PM Luke Martinez <martinezlukerm using gmail.com> wrote:
> > >
> > > Sure, thanks. Along the same lines, if I see that the unconditional
> > > distribution of the SMD estimates is multi-modal or right or left
> > > skewed (perhaps due to extreme outliers), but the unconditional
> > > distribution of the corresponding LRR estimates looks more symmetric
> > > and well-behaved, does that also empirically suggest a mean-sd
> > > relationship in one or more groups?
> >
> > I'm not sure that it implies a mean-sd relationship. But I think it
> > does suggest that LRR might be a more appropriate metric.
> >
> > > PS. Is there a reason for exploring the mean-sd relationship
> > > specifically in the control group?
> >
> > No, you could certainly examine the relationships in the treatment
> > group(s) as well.