Dear Rafael.

I believe the standard errors are computed from (negative inverse of) the Hessian matrix - which is a matrix containing the second-order partial derivatives (or some numerical approximation of them) from the likelihood surface.

These values are measurements of the curvature of the likelihood surface. If the likelihood surface is highly curved (downwards, that is negatively) then this means that the ML solution is much more likely than other nearby possibilities, and the negative inverse of this value is a small quantity - indicating little variance (i.e., uncertainty) in the estimated parameter. Conversely, a large standard error (the square of which is the variance) indicates that the likelihood surface is very flat (that is, it has a very small negative curvature) around the ML solution.

In your particular case broadly overlapping CIs for the parameter estimates (which can be computed as theta+-1.96*SE) of theta probably mean that the 'adaptive peaks' of different regimes can't be distinguished one from the other; whereas a CI for alpha that included zero (for instance) might suggest that a BM model probably better fits the data.

All the best, Liam

Liam J. Revell, Associate Professor of Biology
University of Massachusetts Boston
& Profesor Asociado, Programa de BiologĂ­a
Universidad del Rosario

On 4/4/2018 2:30 PM, Rafael S Marcondes wrote:
Dear all,

I'm writing (again!) to ask for help interpreting standard errors of parameter estimates in OUwie models.

I'm using OUwie to examine how the evolution of bird plumage color varies across habitat types (my selective regimes) in a tree of 229 tips. I was hoping to be able to make inferences based on OUMV and OUMVA models, but I was getting nonsensical theta estimates from those. So I've basically given up on them for now.

But even looking at theta estimates from OUM models, I'm getting really large standard errors, often overlapping the estimates from other selective regimes. So I was wondering what that means exactly. How are these erros calculated? How much do high errors it limit the biological inferences I can make? I'm more interested in the relative thetas across regimes than on the exact values (testing the prediction that birds in darker habitats tend to adapt to darker plumages than birds in more illuminated habitats).

I have attached a table averaging parameter estimates and errors from models fitted across a posterior distribution of 100 simmaps for four traits; and one exemplar fitted model from one trait in one of those simmaps.

Thanks a lot for any help,

*Rafael Sobral Marcondes*
PhD Candidate (Systematics, Ecology and Evolution/Ornithology)

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Louisiana State University
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