Dear list,

I have a tree of 540 species and a binary trait. Using corHMM, I'm fitting
models with one and two rate classes and checking the eigenvalues to ensure
reliable optimization as recommended in the documentation. For models with
one rate class the eigenvalues are positive. However, for most
time-heterogenuous models, even the simplest one, all eigenvalues are zero
(as are the standard errors).

I know very little about the inner workings of ML optimization, so I'm not
sure how to interpret this. Should I treat this type of result as
unreliable optimization? Or do zero eigenvalues mean that the check is
inconclusive? If so, is there another way to check if the parameter
estimates are reliable?

Below is the call to corHMM and the rate matrix.

Thanks!
Teo

# I call corHMM like so:

t100.ER.2rc.rEq <- corHMM(phy = Trees[[100]], data = Salt, rate.cat = 2,
rate.mat = ER.2rc.rEq, node.states = "marginal", root.p = "maddfitz",
n.cores = 4, diagn = TRUE, nstarts = 100)

# The rate matrix has symmetric rate class 1, symmetric rate class 2, and
equal rates of transitions between rate classes irrespective of character
state.

       (0,R1) (1,R1) (0,R2) (1,R2)
(0,R1)     NA      1      2     NA
(1,R1)      1     NA     NA      2
(0,R2)      2     NA     NA      3
(1,R2)     NA      2      3     NA

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