[R-meta] compare multiple "bayesmeta" estimates

[Röver, Christian]

Dear Reza, dear Simon,

yes, indeed, you can also (possibly more easily) work out the solution
via Monte Carlo sampling:


dif <- bma1$rposterior(1e4, tau.sample=FALSE) -
bma2$rposterior(1e4, tau.sample=FALSE)

quantile(dif, probs=c(0.5, 0.025, 0.975))


Note that using "tau.sample=FALSE" accelerates sampling and only
returns the "mu" samples relevant here.

I also spotted an *ERROR* in my previously posted solution (Email from
2020-12-27). In the call to the "convolve()" function, you need to
explicitly specify the function arguments ("mu=..."), otherwise it will
by default pick the first one (which is "tau" here). With this fix, you
get matching results with the numerical convolution and Monte Carlo
approaches -- see the attached code. Sorry for the confusion!

Cheers,

Christian


On Tue, 2020-12-29 at 16:16 -0600, Reza Norouzian wrote:
> Dear Christian,
> 
> Would it be wrong for Simon to do the following to find out the
> difference: 
> 
> dif <- bma2$rposterior(1e3,tau.sample=T)  - 
> bma1$rposterior(1e3,tau.sample=T) and then obtain the HDI of dif to
> see if it contains 0?
> 
> Thank you for your expertise,
> Reza Norouzian
> 
> 
> 
> On Sun, Dec 27, 2020 at 10:30 AM Simon Harmel <sim.harmel using gmail.com>
> wrote:
> > Thank you very much, Christian. I appreciate it. I know and highly
> > appreciate the fact that you've put so much effort into making
> > bayesmeta
> > faster than the MCMC-based equivalents.
> > 
> > But, I really hope that one day we would be able to see still much
> > faster
> > algorithms to enable applying Bayesian meta to large-scale research
> > efforts.
> > 
> > Once again, thank you very much,
> > Simon
> > 
> > On Sun, Dec 27, 2020 at 6:00 AM Röver, Christian <
> > christian.roever using med.uni-goettingen.de> wrote:
> > 
> > > Dear Simon,
> > >
> > > yes, there is a way to investigate the difference of the two as
> > well.
> > > Asking for the difference between the two unknowns (the two mean
> > > parameters) technically means asking for a *convolution* of their
> > > probability distributions. From the "bayesmeta()" output we get
> > the
> > > probability density functions etc, and from these we can derive
> > the
> > > convolution. A method to compute the convolution is described
> > here:
> > >
> > >   C. Roever and T. Friede.
> > >   Discrete approximation of a mixture distribution
> > >   via restricted divergence.
> > >   Journal of Computational and Graphical Statistics,
> > >   26(1):217-222, 2017.
> > >   https://doi.org/10.1080/10618600.2016.1276840
> > >
> > > and R code is provided in the article's supplemental material.
> > >
> > > I attached some R code to show the computations based on the
> > "metafor"
> > > example.
> > >
> > > Cheers,
> > >
> > > Christian
> > >
> > >
> > >
> > > On Sat, 2020-12-26 at 13:49 -0600, Simon Harmel wrote:
> > > > Dear Christian,
> > > >
> > > > Thank you very much. To be clear, you're suggesting a meta-
> > analysis
> > > > of the subgroup meta-analyses, correct?
> > > >
> > > > Well, in my case, I have way too many subgroups, so there will
> > be
> > > > many pairwise comparisons. I wonder if there is a way to get
> > the
> > > > large posterior samples from each subgroup' summary effect and
> > > > subtract it from the large posterior samples from another
> > subgroup
> > > > summary effect etc.?
> > > >
> > > > Perhaps, then we can see if the HDI of the posterior of
> > difference
> > > > includes "0"?
> > > >
> > > > Is this possible and/or reasonable given that my goal is to see
> > if
> > > > one subgroup is "different" from another one or not?
> > > >
> > > > Thank you,
> > > > Simon
> > > >
> > > > On Sat, Dec 26, 2020 at 12:38 PM Röver, Christian <
> > > > christian.roever using med.uni-goettingen.de> wrote:
> > > > > Dear Simon,
> > > > >
> > > > > you can essentially do an analogous analysis (in two stages)
> > using
> > > > > the
> > > > > "bayesmeta" package. Doing the one-stage meta-regression
> > approach
> > > > > is
> > > > > not (yet) possible with bayesmeta, but it should be possible
> > via
> > > > > "rjags" (of required).
> > > > >
> > > > > For the two-stage approach, we then only need to use a normal
> > > > > approximation for the results from the 1st-stage analyses and
> > > > > proceed
> > > > > from there.
> > > > >
> > > > > I attached some example R code based on the quoted "metafor"
> > > > > example.
> > > > >
> > > > > Cheers,
> > > > >
> > > > > Christian
> > > > >
> > > > >
> > > > >
> > > > > On Sat, 2020-12-26 at 10:46 -0600, Simon Harmel wrote:
> > > > > > Hello All,
> > > > > >
> > > > > > Using "bayesmeta" package, I want to compare multiple
> > estimates
> > > > > of
> > > > > > independent Meta-Analyses (i.e., Subgroups).
> > > > > >
> > > > > > In metafor, I know we can do this: (
> > > > > >
> > > > >
> > > 
> > http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates
> > > > > > )
> > > > > >
> > > > > > But I have fit my models in the "bayesmeta" package, so I
> > was
> > > > > > wondering how to compare across my "bayesmeta" models?
> > > > > >
> > > > > > Thanks,
> > > > > > Simon
> > > > > >
> > > > > >
> > >
> > 
> >         [[alternative HTML version deleted]]
> > 
> > _______________________________________________
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> > R-sig-meta-analysis using r-project.org
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