New version of phyl.RMA for reduced major axis regression

I just posted a new version of phyl.RMA which also computes r², T, df, and a P value for the test. The r² is just the squared phylogenetic correlation. The other values are based on McArdle (1987). Direct link to code is here.

By default, the function tests the null hypothesis that the RMA slope is equal to 1.0. It is possible to change this default; however it is generally not possible to test for β=0.0 as this would only be true if σ_Y² was zero.

Here's a quick illustration of how it works, using functions in the geiger package to generate data under the null hypothesis for β (that is, β=1.0), but with λ=0.7:

> require(phytools)
> require(geiger)
> source("phyl.RMA.R")
> tree<-pbtree(n=150)
> X<-sim.char(lambdaTree(tree,0.7), model.matrix=matrix(c(2,1.5,1.5,2),2,2))[,,1]
> rma<-phyl.RMA(tree=tree,X[,1],X[,2],method="lambda")
> rma
$RMA.beta
[1] 0.1901904 1.0659599
$V
         x        y
x 2.305487 1.913151
y 1.913151 2.619657
$lambda
[1] 0.7334247
$logL
[1] -604.2649
$test
         r2           T          df           P
  0.6060265   1.2380363 115.5828809   0.2182114
$resid
             [,1]
t1   -1.543336686
t2    0.250290514
t3   -1.147190156
t4   ...