[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 08:49:50 CET 2023
Hello all,
According to:
https://www.metafor-project.org/doku.php/plots:funnel_plot_variations I
think it could be the argument:
-
yaxis="seinv" for the inverse of the standard errors
Is what gives the 1/SE for each element in the vector of effect sizes in
the x-axis.
How can I "stand alone"—that would be outside the metafore package or not
using the funnel function—to plot the same scatterplot of effect sizes
(x-axis) against 1/SE (y-axis) in communion and a simple R scatter
plot—without the funnel background—and afterwards use it to further cluster
by coloring or using shapes ("pch") the effect sizes according to different
categorical variables in the data frame?
Thanks a lot for your help.
Kind regards,
Gabriel
On Tue, Nov 7, 2023 at 9:13 AM Gabriel Cotlier <gabiklm01 using gmail.com> wrote:
> 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
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>>> > > 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
>>> >
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