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

Thu, Jul 20, 2023 7:28 AM

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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     >
     >     --
     >     Michael
     > http://www.dewey.myzen.co.uk/home.html

    <http://www.dewey.myzen.co.uk/home.html>

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

Thread (9 messages)