[R-meta] question on scatter plot of estimates (Fisher's Z) against the standard error
Gabriel Cotlier
g@b|k|m01 @end|ng |rom gm@||@com
Tue Nov 7 08:13:58 CET 2023
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 using 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 Rücker <
> gerta.ruecker using 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
>>
>>
>>
>> UNIVERSITÄTSKLINIKUM FREIBURG
>> Institute for Medical Biometry and Statistics
>>
>> Dr. Gerta Rücker
>> Guest Scientist
>>
>> Stefan-Meier-Straße 26 · 79104 Freiburg
>> gerta.ruecker using uniklinik-freiburg.de
>>
>> https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker
>>
>>
>> -----Ursprüngliche Nachricht-----
>> Von: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> Im
>> Auftrag von Gabriel Cotlier via R-sig-meta-analysis
>> Gesendet: Donnerstag, 20. Juli 2023 16:28
>> An: Michael Dewey <lists using dewey.myzen.co.uk>
>> Cc: Gabriel Cotlier <gabiklm01 using gmail.com>; R Special Interest Group for
>> Meta-Analysis <r-sig-meta-analysis using 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 using 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 using dewey.myzen.co.uk
>> > > <mailto: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>
>> > > > <mailto: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>
>> > > > <http://www.dewey.myzen.co.uk/home.html
>> > > <http://www.dewey.myzen.co.uk/home.html>>
>> > > >
>> > > >
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>> > > <
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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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>> > Michael
>> > http://www.dewey.myzen.co.uk/home.html
>> >
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