[R-meta] question on scatter plot of estimates (Fisher's Z) against the standard error

Thu Jul 20 06:55:20 CEST 2023

Dear Michael,

I think you are completely right, in the fact, the plot I am producing is
indeed valid for the purpose for which I want to use it, meaning it is
representative of the relationship I want to show. Therefore, I assume that
the plot I am getting, is supposed to be sufficient.

However, I receive from the function metafore:: funnel (model), for a model
without modierators, a very nice representation of the scarring of the
observed outcomes or the estimates (x axis), as a function of the SE (e.i.,
square root of the sampling variance, SE assumef to have a pseudo confidence
interval region drawn around each of its values). While, when I plot by
myself
x = observed outcomes
y = square root of the sampling variance,

Then the plot shows that:
a.  the scattering of the points appears upside down with respect to the
output of the function metafore:: funnel (model),
b. the scale of the y axis, instead of having a defined top at zero and
from there values are represented downwards, the scale is different.

Anyways, I started thinking that in any case, such a difference in the plot
I am doing by myself is not necessarily wrong, but is just a different way
of representing the data. Just the scattering of the points in one  case
looks like the upside down scattering of the other. And I assume this is
because maybe the function metafore::funnel() applies some operation on the
square root of the mean (y axis) that I presume is the calculation of the
aforementioned pseudo confidence interval for each value, but I am not sure.

Thanks a lot for your response.
Kind regards,
Gabriel

On Wed, Jul 19, 2023 at 7:20 PM Michael Dewey <lists using dewey.myzen.co.uk>
wrote:

> I am sorry Gabriel but I do not understand why the plot you say you
> produced fails to do what you say you want.
>
> Michael
>
> On 19/07/2023 10:59, Gabriel Cotlier wrote:
> > Hello Michael,
> > Thank you very much for your response.
> > I just would like to show that the of data set I have has high
> > uncertainty given that no possible pattern is observable or detectable
> > and no order is possible to visulize in the scattering,
> > I thought that a plot with x axis = fisher's z observed
> > outcomes (estimates) and y axis = standard error or any other measure of
> > uncertainty could at least visually demostrate that assumption.
> > If such a lack of pattern or high uncertainty in the data set can also
> > be demonstrated numerically, even better.
> > Kind regards,
> > Gabriel
> >
> > On Wed, Jul 19, 2023 at 12:29 PM Michael Dewey <lists using dewey.myzen.co.uk
> > <mailto:lists using dewey.myzen.co.uk>> wrote:
> >
> >     Dear Gabriel
> >
> >     I am not realy sure what you are trying to do but one point which
> >     occurs
> >     to me is that forest plots are conventional plotted with small
> >     values of
> >     standard error at the top.
> >
> >     Michael
> >
> >     On 19/07/2023 06:07, Gabriel Cotlier via R-sig-meta-analysis wrote:
> >      > Dear all,
> >      >
> >      > I have already posted this question with no response.
> >      > Maybe this time I am luckier and someone with more knowledge than
> >     me in the
> >      > Metafor package can answer me.
> >      >
> >      > In a nutshell, what I would like is to be able to produce a
> >     scatter plot of
> >      > the observed oucomes or the estimates, in my case Fisher's z for
> >     the x axis
> >      > and the standard error in the y axis, with the standard error
> >     (SE) the
> >      > same as it appears when running the funnel() function for a
> >     funnel plot
> >      > with the model (without moderators) as the input argument.
> >     Actually, it is
> >      > a funnel plot without the background of the funnel distribution
> >     but just
> >      > the scatter of points, that is suppressing the funnel
> distribution on
> >      > the background.
> >      >
> >      > I tried to do so in agreement with the definition of SE used for
> >     the funnel
> >      > plot in the package Vignette published at Journal of Scientific
> >     software in
> >      > page 26:
> >      >
> >      > "*For models without moderators, the figure shows the observed
> >     outcomes on
> >      > the horizontal axis against their corresponding standard errors
> >     (i.e., the
> >      > square root of the sampling variances) on the vertical axis. A
> >     vertical
> >      > line indicates the **estimate based on the model. A pseudo
> confidence
> >      > interval region is drawn around this value with bounds equal to
> >     ±1.96 · SE,
> >      > where SE is the standard error value from the vertical axis.*"
> >      >
> >      >
> >      > I tried to reproduce the vertical axis (y) using the square root
> >     of the
> >      > sampling variable, but the result was an upside down scaling of
> the
> >      > observed outcomes or estimates on a different y scale for the x
> >     ticks. The
> >      > plot seems to have similarities with the funnel plot from the
> >     funnel()
> >      > function, but it is not exactly the same without the background
> >     of the
> >      > funnel distribution graphic. Maybe the problem could be that in
> the
> >      > funnel() function, contrary to my simple attempt to imitate it
> >     with the
> >      > square root of the sampling variable, the pseudo confidence
> >     interval is
> >      > estimated for each value? Could this be the reason?
> >      >
> >      >
> >      > If so, how could I reproduce the funnel () function plot without
> >     the funnel
> >      > distribution graphic in the background and just the scattering of
> the
> >      > points using the same pseudo-confidence interval?
> >      >
> >      >
> >      > Thanks a lot for your help and assistance.
> >      >
> >      > Kind regards,
> >      >
> >      > Gabriel
> >      >
> >      >       [[alternative HTML version deleted]]
> >      >
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> >
> >     --
> >     Michael
> >     http://www.dewey.myzen.co.uk/home.html
> >     <http://www.dewey.myzen.co.uk/home.html>
> >
> >
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