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

Dear Greta and colleges,

As can be seen below, Greta has provided a nice solution to a problem I
could not solve before, which is to have as an output of metafor's package
function funnel() for plotting the funnel plot without the background of
the funnel itself, which I very slightly modified as follows:

###################
##
##.  CODE FUNNEL
##
###################

## data
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)

## model
funnel_all <- rma.mv(yi,  vi,  data=dat)

## get max and min values for plot
#funnel_all$yi
#min(funnel_all$yi)
#max(funnel_all$yi)

## funnel plot
f1 <- funnel(funnel_all,
             back = "white",
             # shade = "white",
             yaxis = "seinv",
             level = 0,
             # ylim = c(1, 5),
             refline=0,
             main="my plot",
             ylab = "Presicion (1/SE)",
             xlim = c(0.53,1.5))
# shade = c("white", "gray55", "gray75"),
# refline = 0)
# bg = "grey")
# legend = TRUE)
#grid(NULL, NULL,lwd = 1.6)
abline(h=c(9.849, 11.316, 12.783, 14.249, 15.716 ), col="grey", lwd=1,
lty=3)
abline(v=1, col="blue", lwd=2)
abline(v=c( 0.6, 0.8, 1, 1.2, 1.4), col="grey", lwd=1, lty=3)


This has been a very efficient solution for my problem of getting exactly
the same funnel plot as the result of the metafore package
function funnel() without the funnel as a background. However, now I am
facing the challenge of having plotted the same funnel plot as the
output from the metafor's funnel() function without the background but
without the option of clustering by coloring or giving different point
shapes to the effect szes (points in the funnel plot) according to a
categorical in my data frame. I assume?probably wrongly?that for this task
I would have to reproduce the same funnel plot as is output from the funnel
plot function in the metafore package without the funnel background, as in
the code above, and use my data frame with the categorical variables to
color the points or give them different shapes and sizes using the
categorical variables in my data frame. Now the funnel plot function plots
in the x-axis the effect sizes, something I can easily get from my data
frame, but in the y-axis it uses 1/standad error (or 1 / SD). The
problem is that, as far as I understand, the standard error (SE)
corresponds to the standard deviation, or the R function sd() which gives
one value per input vector. Therefore, for some reason, plotting the effect
sizes (a vector class numeric) in the x-axis and 1/sd(effect_sizes) will
give me a number, not a vector of the same length as the effect sizes.

*Therefore, how could one reproduce the same funnel plot as in the
metafore function (without the funnel background, just a scatterplot)
with an x-axis composed of the vector of effect sizes and a y-axis with
another vector corresponding to 1/stands error (1/SE) of each element in
the x-axis--If 1/SE is is equal to 1/sd(efect_sizes) which is a scaler and
not a vector ?*

I think maybe this could be achieved somehow by giving, in the y-axis, a
kind of *"element-wise 1/SE"* to each element in the x-axis; that would
be an value corresponding to 1/SE to each of the elements in the vector of
effect sizes in the x-axis. Could this be the idea behind the funnel plot
function with 1/SE on the y-axis?

If so, can this be somehow achieved following the example provided by
Greta below?

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)

Thanks a lot for your help and guidance.
Kind regards,
Gabriel

On Fri, Jul 21, 2023 at 9:28?AM Gabriel Cotlier <gabiklm01 at gmail.com>
wrote:

Dear Greta,

Thank you very much.
The code you provided for the funnel plot is exactly what I was looking
for.

I just changed my refline to zero and adjusted the xlim to the interval
[-4 6], so it is exactly the same as the metafor::funnel plot but without
all the background, keeping only the scattering of the points.

Thanks a lot again.
Kind regards,
Gabriel



On Thu, Jul 20, 2023 at 11:21?PM Dr. Gerta R?cker <
gerta.ruecker at uniklinik-freiburg.de> wrote:

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]]
     >      >
     >      > _______________________________________________
     >      > R-sig-meta-analysis mailing list @

     > R-sig-meta-analysis at r-project.org

    <mailto:R-sig-meta-analysis at r-project.org>

     >     <mailto:R-sig-meta-analysis at r-project.org

    <mailto:R-sig-meta-analysis at r-project.org>>

     >      > To manage your subscription to this mailing list, go

to:

     >      >