Krzystof,
       Thank you for your reply.  It is promising that you think that Li's
method should work for imputed mantel results.  That said, I am a bit over
my head with the math in the Li et al reference.  Could you (or anyone on
this list) provide an R-code example of how D would be calculated from the
output of several mantel tests?

Also, and forgive my ignorance if this statement is coming from the wrong
direction, It is my understanding that mantel P values are generally
calculated by actually permuting the rows of the similarity matrix and
re-running the mantel test a given number of times (usually 1000).
Accordingly, as far as I can tell there is no explicitly generated F value
corresponding to a mantel p value.  It seems like Li's method assumes I am
generating P from an F table.  Would it be appropriate to back calculate F
from P, k and m?

Thanks again,
Jacob



On Sun, Aug 18, 2013 at 2:19 PM, Krzysztof Sakrejda <
krzysztof.sakrejda@gmail.com> wrote:

> Hi Jacob, comments below.
>
> On Aug 18, 2013 2:31 PM, "Jacob Cram" <cramjaco@gmail.com> wrote:
> >
> > Dear List,
> >       I have an environmental data set with several missing values that I
> > am trying to relate to a community structure data set using a mantel
> > test.   One solution to the missing data problem seems to be multiple
> > imputation; I am using the Amelia package. This generates several (five
> in
> > this example) imputed data sets.  I can run mantel on each of these and
> > come up with five similar but not identical solutions.  I figure I can
> > average the mantel rho values.  However, I am not sure what to do about
> the
> > P values. From looking around online, it looks like I shouldn't take the
> > average of p values.  I found this reference <
> >
> http://missingdata.lshtm.ac.uk/index.php?option=com_content&view=article&id=164:combining-p-values-from-multiple-imputations&catid=57:multiple-imputation&Itemid=98
> >
> > that seems to have promising suggestions, but I can't seem to figure out
> > how I'd implement any of these in R.
>
> So following that link and reading the Li et al. reference it looks as
> though the procedure is well described at the top of page 71. You get your
> parameter estimate from the usual procedure. The test statistic, written as
> "D", is the distance between the null value and the estimated value with
> some scaling specified in eq. 1.17. They use the F distribution and k and m
> (the number of imputations) degrees of freedom. I don't think you need to
> reinvent some inferior ecologists-only procedure for this.
>
> Krzysztof
>
> I was hoping somebody might have a
> > suggestion for how I could combine my p values.  One option, I think
> would
> > be to take the highest (worst) p value (in the example below, this would
> be
> > p = 0.012).  However for large numbers of imputations, I am believe that
> > this method might be to conservative.  Another option might be to take
> the
> > p value corresponding to the median rho score (in the example below this
> > would be p =0.008).   Thoughts?
> > -Jacob
> >
> >
> > ##Example Code Below
> > require(Amelia)
> > require(vegan)
> > require(ecodist)
> >
> > ##Species data matrix with environmental data that are missing some
> values.
> > data(varespec)
> > data(varechem)
> > varechem.missings <- varechem[,c("N", "P", "K")]
> > varechem.missings[c(1,5, 7, 15, 20),1] <- NA
> > varechem.missings[c(1,2, 9, 21), 2] <- NA
> >
> > #I multiply impute the missing values with the Amelia package
> > imps <- 5
> > #imps <- 25
> > varechem.amelia <- amelia(varechem.missings, m = imps)
> >
> >
> > #for each imputation of the environmental data I run a mantel test and
> save
> > #the results to mresults
> > mresults <- NULL
> >
> > for(i in 1:imps){
> > varespec.dist <- vegdist(varespec)
> > varechem.am.dist <- dist(varechem.amelia$imputations[[i]])
> > mresults <- rbind(mresults,
> > (ecodist::mantel(varespec.dist~varechem.am.dist)))
> > }
> >
> > mresults
> >
> > ##        mantelr pval1 pval2 pval3 llim.2.5% ulim.97.5%
> > ## [1,] 0.2137656 0.008 0.993 0.008 0.1015176  0.3389979
> > ## [2,] 0.2162388 0.011 0.990 0.011 0.1207528  0.3346554
> > ## [3,] 0.2149556 0.012 0.989 0.016 0.1319943  0.3279028
> > ## [4,] 0.2101820 0.009 0.992 0.012 0.1217293  0.3288272
> > ## [5,] 0.2135279 0.006 0.995 0.006 0.1130386  0.3359864
> >
> > #based on these results what would be a reasonable p value to report for
> > the environmental parameters relating to the community structure?
> >
> > ##end example
> >
> >         [[alternative HTML version deleted]]
> >
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> > R-sig-ecology@r-project.org
> > https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>

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