[ADMB Users] Restricting magnitude of random effects estimates, achieving convergence of RE models

dave fournier otter at otter-rsch.com
Thu Aug 5 03:52:36 PDT 2010

The reason that the bounded random effects vector was not carried on 
with is that I realized it is the wrong approach. the right general 
approach I believe is to start with a standard normal random effect
and transform it to what you want. So for a log-normal you start with

      u   and transform it to exp(sigma*u)

By start with I mean that the RE is parameterized by u and the log-prior
is 0.5*u*u.

In this case Hans suggestion of the logistic makes sense. You go from

      u  to    logistic(sigma*u)

I guess the reason you don't want the logistic is that you want the
RE to look like normal near 0.  So then rather than the logistic we need 
a function

          F(x)   =      x  if |x|< |C-delta|

          F(x)  --->  C  as x---> infinity

          F(x)  ---> -C   as x --> -infinity

   and use  u --->F(sigma*u)

    So it is like a logistic but linear near 0.

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