Spencer,

I tried the mixed effects approach you suggest using the random effects
module of
AD Model Builder: (http://www.otter-rsch.ca/admbre/admbre.html). What are
94 unbounded parameters in Schnute et al (1998), now become realizations
of a Gaussian random variable, with the corresponding standard deviation
being
estimated as a parameter. The approach works, but the computation time is
increased substantially. This is however  understandable
as the computational problem is a very different one. The likelihood
function
now involves an integral in dimension 94, which I believe cannot be broken
into
a product of lower dimensional integrals as is usual for clustered data (the
reason being the recursive nature of the population dynamics).

hans

_______________________________



Spencer Graves wrote:

>     Have you considered nonlinear mixed effects models for the types
>of problems considered in the comparison paper you cite?  Those
>"benchmark trials" consider "T years of data ... for A age classes and
>the total number of parameters is m = T+A+5".  Without knowing more
>about the problem, I suspect that the T year parameters and the A age
>class parameters might be better modeled as random effects.  If this
>were done, the optimization problem would then involve 7 parameters, the
>5 fixed-effect parameters suggested by the computation of "m" plus two
>variance parameters, one for the random "year" effects and another for
>the random "age class" effect.  This would replace the problem of
>maximizing, e.g., a likelihood over T+A+5 parameters with one of
>maximizing a marginal likelihood over 2+5 parameters after integrating
>out the T and A random effects.
>
>     These integrations may not be easy, and I might stick with the
>fixed-effects solution if I couldn't get answers in the available time
>using a model I thought would be theoretically more appropriate.  Also,
>I might use the fixed-effects solution to get starting values for an
>attempt to maximize a more appropriate marginal likelihood.  For the
>latter, I might first try 'nlmle'.  If that failed, I might explore
>Markov Chain Monte Carlo (MCMC).  I have not done MCMC myself, but the
>"MCMCpack" R package looks like it might make it feasible for the types
>of problems considered in this comparison.  The CRAN summary of that
>package led me to an Adobe Acrobat version of a PPT slide presentation
>that seemed to consider just this type of problem (e.g.,
> http://mcmcpack.wustl.edu/files/MartinQuinnMCMCpackslides.pdf).
>
>     Have you considered that?
>     Hope this helps.
>     Spencer Graves

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