[ADMB Users] some light reading

[otter]

This is a propos a question by Maunder a while back about whether random 
effects would
ever be included into multifan CL.

Every once and a while I read a fish model paper to convince myself that 
nothing ever gets any better.

This is a link to a paper adding random effects to some structures in 
the fish model Stock synthesis.


http://icesjms.oxfordjournals.org/content/72/1/178.short

The authors eschew the use of ADMB's random effects package in favour of 
an ad hoc approach
employing ADMB together with its Hessian calculations suitably 
modified.  They justify this approach with the
statement.

. Similarly, implementing a model in ADMB-RE requires
a large overhead of time and expertise due to the practical necessity of
finding a “separable” formulation of the population model (Bolker
et al., 2013) and still may take a considerable amount of time
during optimization.

This is more or less completely false.   First it is not necessary to 
have a separable formulation
of the model.  It is quite feasible to have a model with thousands of 
random effects without
invoking separability.   For a fish model where the random effect (say a 
catchability deviation)
affects the population for the rest of the time after it occurs 
separability os of no use anyway.

The statement about "may take a considerable amount of time is true" for 
general RE models
of course but they are considering an application where  they integrate 
over all but a small
number of variance parameters (say up to 3 or 5).   In ADMB-RE this is 
equivalent to declaring
almost all the parameters to be of type random effect.   This has been 
discussed before
(although the concept seemed to baffle Bates.)  in the context of 
generalizing restricted maximum
likelihood estimation.

The point is that ADMB-RE does the parameter estimation by first doing 
an inner optimization over the
random effects.   This is essentially equivalent to the authors use of 
ADMB.  The difference is that
once the inner optimization is done ADMB-RE calculates the Hessian in a 
much more efficient manner
than  ADMB. It also uses this hessian to "polish" the estimates so that 
they are much closer to the
minimizing values in the sense that the max gradient magnitude is 
typically reduced from something like
1.e-4 to 1.e-12.   It then also computes the derivatives of the function 
with respect to the variance parameters
in a very efficient manner.   This enables one to use derivative based 
minimization rather than the
incredibly inefficient Nelder Mead  (which may work for a really well 
behaved problem with 3 parameters
but will never extend well to more parameters or more badly conditioned 
optimization procedures.

So ADMB-RE   is already almost perfectly equipped to handle this model.  
A small extension is needed to
permit it to have bounded random effects compatible with the bounded 
parameters in ADMB.