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

Dear Gabriel,

Both plots are correct and equivalent (though I like the metafor plot much
more). If it is only to get rid of the confidence region, why don't you use
the funnel() function of metafor and suppress all elements you don't want?
For example, try (object funnel_all taken from your R code, fictitious
data coming from me, as you did not provide them!)

ri <- c(0.5, 0.6, 0.7, 0.8, 0.9)
ni <- c(100,110,150,200,250)
dat <-escalc(measure = "ZCOR",  ri = ri, ni = ni)

funnel_all <- rma.mv(yi,  vi,  data=dat)
funnel(funnel_all, back = "white", shade = "white", level = 0, xlim =
c(0.5,1.6), refline = 2)

The xlim argument is used to fix the x-axis range, while putting the
refline outside the visible region (simply a trick, I couldn't find an
argument to determine the refline's color). You may also change the y-axis
range, e.g.,

funnel(funnel_all, back = "white", shade = "white", level = 0, xlim =
c(0.5,1.6), refline = 2, ylim = c(0.06, 0.105))

if you think this makes sense. With respect to the inverted axis, see
Michael's post.

Best,
Gerta



UNIVERSIT?TSKLINIKUM FREIBURG
Institute for Medical Biometry and Statistics

Dr. Gerta R?cker
Guest Scientist

Stefan-Meier-Stra?e 26 ? 79104 Freiburg
gerta.ruecker at uniklinik-freiburg.de

https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker


-----Urspr?ngliche Nachricht-----
Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> Im
Auftrag von Gabriel Cotlier via R-sig-meta-analysis
Gesendet: Donnerstag, 20. Juli 2023 16:28
An: Michael Dewey <lists at dewey.myzen.co.uk>
Cc: Gabriel Cotlier <gabiklm01 at gmail.com>; R Special Interest Group for
Meta-Analysis <r-sig-meta-analysis at r-project.org>
Betreff: Re: [R-meta] question on scatter plot of estimates (Fisher's Z)
against the standard error

Dear Michael,
Here is the code below:
Thanks a lot.
Kind regards,
Gabriel

## Transformation of Pearson's Product-moment correlation coefficient (r)
to Fisher's Z
dat <-escalc(measure = "ZCOR",
             ri = ri,
             ni = ni,
             data = dat)

##
funnel_all <- rma.mv(yi,
                     vi,
                     # mods = ~ Type,
                     random = ~ 1 | Article / Sample_ID,
                     data=dat)

funnel_all
## funnel plot form metafor
funnel(funnel_all)

## Variance : from general model extracted
vi_data <-funnel_all$vi

## Estimates : from general model extracted estimates
yi_data <-funnel_all$yi[1:150]

## calculate standard error SE: square root of the variance
SE<- sqrt(vi_data)

# estimates
E <-funnel_all$yi

## construct data frame
df <- data.frame (Estimates = c(E), Standsrd_Error = c(SE))
View(df)
library(ggplot2)
## Scatter plot
scaleFUN <- function(x) sprintf("%.2f", x)
p<- ggplot(df, aes(x=Estimates, y=Standsrd_Error)) +
  geom_point(aes(size = Estimates), alpha=0.7,  color="#2568E6")+
  scale_size_area() +
  labs(x = "Fisher's z",
       y = "Standard Error (SE)")+
  theme(plot.title = element_text(hjust = 0.5))+
 # theme(plot.margin = unit(2 ,8, 8, 2), "cm"))+
  scale_y_continuous(n.breaks = 12,labels=scaleFUN)+
  scale_x_continuous(n.breaks = 12,labels=scaleFUN)+
  geom_vline(xintercept = 0)+
  theme(axis.text.y = element_text(size = 15))+
  theme(axis.text.x = element_text(size = 15))+
  theme(axis.title.y = element_text(size = 15))+
  theme(axis.title.x = element_text(size = 15))+
  ggtitle( "Fisher's z vs. Standard Error")+
  theme(plot.title = element_text(size = 17, face = "bold"))+
  theme(legend.text = element_text(size = 15))
  p
png(filename = "myplot.png", width = 28,  height = 18 ,units = "cm" , res
=100 )
print(p)
dev.off()



On Thu, Jul 20, 2023 at 4:51?PM Michael Dewey <lists at dewey.myzen.co.uk>
wrote:

Dear Gabriel

Comments in-line

On 20/07/2023 05:55, Gabriel Cotlier wrote:

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),

I have already answered that one in a previous post. It is just the
convention

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.

Without your code it is hard to tell but I suspect you are not plotting
what you think you are. Are you plotting the inverse of the se?

Michael

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 at dewey.myzen.co.uk
<mailto:lists at 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 at dewey.myzen.co.uk <mailto:lists at dewey.myzen.co.uk>

     > <mailto:lists at dewey.myzen.co.uk

    <mailto:lists at 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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