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

[Luke Martinez]

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.