[R-sig-ME] fixed effects (co)variance matrix from MCMCglmm

Jarrod Hadfield j.hadfield at ed.ac.uk
Mon Nov 19 16:09:34 CET 2012


sqrt(diag(v)) should give the posterior standard deviations (akin to  
the standard errors)

sqrt(diag(v))/nrow(model$Sol) gives the standard error on the  
posterior mean given independence of the stored MCMC samples. Its a  
measure of the Monte Carlo error due to finite chain length.



Quoting Ben Bolker <bbolker at gmail.com> on Mon, 19 Nov 2012 14:58:37  
+0000 (UTC):

> Katie Colborn <benton at ...> writes:
>> Hi:
>> How do I obtain the variances (and covariances) for the fixed effects
>> from an MCMCglmm object? In a
>> frequentist setting I would simply use algebra to obtain it from
>> the confidence intervals if it was not
>> provided; however, I'm not sure if this is equivalent in
>>  Bayesian credible intervals. Is it as simple as:
>> coeff - 1.96*SE = lower 95% CI?
>> Or is it sd(model$Sol)[1:3]?
>> If you solve for SE in the equation above it is
>> not equal to sd(model$Sol) (even after dividing by root n).
>> Thanks for your help!
>   You have to be careful to distinguish between the standard deviation
> and the standard error in this case, and to be aware that the posterior
> distributions may not be multivariate normal.
>   *If* the posteriors are multivariate normal, then
> v <- var(model$Sol)  should give the variance-covariance matrix,
> and sqrt(diag(v)/nrow(model$Sol))  should give the standard errors.
>   If they're not multivariate normal (or at least if the marginal
> posteriors aren't normal) then the credible intervals won't line
> up with +/- 1.96*SE ...
>   If in doubt, take a look at some density plots and scatterplots
> of the posterior densities to get a better sense of what's going on.
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