glmmTMB: variance-covariance matrix parameterization
Starting at https://github.com/glmmTMB/glmmTMB/blob/master/glmmTMB/src/glmmTMB.cpp#L151 for an nxn variance-covariance matrix, we have the first n parameters as the logarithms of the standard deviation. The remaining parameters fill in the lower triangle (in column-major order) of the Cholesky factor of the correlation matrix: information on this is at http://kaskr.github.io/adcomp/classUNSTRUCTURED__CORR__t.html So, for a 2x2 unstructured variance-covariance matrix, the first two parameters are the log-sd, the third parameter is the correlation. I'm adding this to the documentation for ?VarCorr ... On Sun, Aug 14, 2016 at 5:50 PM, Sophia Kyriakou
<sophia.kyriakou17 at gmail.com> wrote:
Hi all,
Does anyone know what is the parameterization that glmmTMB uses for the
variance-covariance matrix in the case of generelized linear mixed models?
I can tell that when fitting a generalized linear mixed model with a random
intercept, where the random effects are normally distributed with zero mean
and variance sigma^2, glmmTMB estimates theta = log(sigma) and then returns
sigma^2.
But what is the parameterization for example in the 2 x 2 random-slopes
case?
Let the 2 x 2 variance-covariance matrix have elements ( sigma^2_{1},
sigma_{12}, sigma_{12}, sigma^2_{2} ).
glmmTMB returns three theta parameters (theta_1, theta_2, theta_3), where
theta_1 = log(sigma_1)
theta_2 = log(sigma_2)
but I don't know what the relationship between theta_3 and sigma_{12} (or
the correlation rho) is.
I know that I can extract thetas using fitTMB$sdr$par.fixed and sigmas
using matrix(unlist(VarCorr(fitTMB)),2,2), where fitTMB is the model fitted
via glmmTMB, but I would like to understand the parameterization used.
Thank you in advance.
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