[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
Hi,
sqrt(diag(v)) should give the posterior standard deviations (akin to
the standard errors)
sqrt(diag(v))/nrow(model$Sol) gives the standard error on the
posterior mean given independence of the stored MCMC samples. Its a
measure of the Monte Carlo error due to finite chain length.
Cheers,
Jarrod.
Quoting Ben Bolker <bbolker at gmail.com> on Mon, 19 Nov 2012 14:58:37
+0000 (UTC):
> Katie Colborn <benton at ...> writes:
>
>>
>> Hi:
>>
>> How do I obtain the variances (and covariances) for the fixed effects
>> from an MCMCglmm object? In a
>> frequentist setting I would simply use algebra to obtain it from
>> the confidence intervals if it was not
>> provided; however, I'm not sure if this is equivalent in
>> Bayesian credible intervals. Is it as simple as:
>>
>> coeff - 1.96*SE = lower 95% CI?
>>
>> Or is it sd(model$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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