[ADMB Users] difference between ADMB-RE and R/mgcv in SEs for smoother coefficients in a GAM fitted by maximum likelihood

dave fournier davef at otter-rsch.com
Thu Nov 29 09:17:23 PST 2012

First, you can find the code that does the calculations in mod_sd.cpp 
and getbigs.cpp.

I guess there are two questions here. One is whether the method used in 
ADMB is reasonable.
The second is whether it is carried out without error.  The method is 
quite simple.
First it is assumed that the covariance matrix for the random effect u 
given the value of the fixed effects
is equal to th inverse of the Hessian of the posterior distribution.
Call this matrix S .Another term is added to this.
The extra term corresponds to the uncertainty in the values of the fixed 
effects.  This is calculated
in a frequentist way.  The mode of the posterior distribution uhat(x) is 
a vector of
dependent variables. denoting the dervative of these wrt x by uhat'(x), 
their covariance
matrix via the delta method is

                       uhat'(x) * H * uhat'(x)

and their correlation with x is give by

                        H * uhat'(x)

The entire correlation matrix is

                              H H*uhat'(x)

                          trans(H*uhat'(x))                 S+ uhat'(x) 
* H * uhat'(x)

I guess we should look at some simpler cases and see if this is 
reasonable and correct.

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