[ADMB Users] ADMB and hierarchical (multi-level) models

[Saang-Yoon]

Dear ADMB users.

While I have been obsessed with this problem, I come up with the idea
of using the excellent package of “PBSadmb” created by Dr. John
Schnute and his colleague at Pacific Biological Science Center, B.C.,
Canada.  PBSadmb enables us to run an ADMB program within R.  If given
hierarchical models, we can break the whole process into a series of
sub-set models.  Using the package of PBSadmb, we can run the subset
ADMB models inside R.  In doing this way, estimates of hyper
parameters are not affected by data and parameters at lower levels,
and those hyper parameter estimates affect along only one way (i.e.,
only toward the lower levels).  Thanks to PBSadmb, now we can combine
ADMB and R together.  I was VERY happy using PBSadmb, and I greatly
thank Dr. John Schnute  and his colleague for the package as well as
ADMB developer (Dr. Fournier).

However, if someone has a better idea about how to code hierarchical
models in ADMB, please let me know.

Saang-Yoon


On Aug 16, 7:33 pm, Saang-Yoon <shyu... at gmail.com> wrote:
> Hello, Paul.
>
> Thank you very much for your comments and suggestions.  I have not yet
> tried to do the MCMC option.  I will try to do so.  However, the MCMC
> algorithm in ADMB is Metropolis-Hastings method, and it may not be
> promising to a hierarchical structure.  Gibbs method seems better for
> a hierarchical structure.
>
> By the way, the hard core of my inquiry was a problem that estimates
> of hyper parameters are affected by data and parameters at a "LOWER"
> level although they must NOT.
>
> Again thank you,
>
> Saang-Yoon
>
> On Aug 16, 11:11 am, Paul Conn <Paul.C... at noaa.gov> wrote:
>
>
>
> > Hi Saang-Yoon,
>
> > I agree that hierarchical models potentially pose problems for
> > MLE/maximum a posteriori (MAP) estimation and inference (possibly
> > leading to bias and overly precise estimates), but wouldn't MCMC
> > estimates be okay because you're integrating over the plausible range of
> > values for unobserved data (in a complete data sense)?  Have you tried
> > fitting models with the 'mcmc' option in ADMB?
>
> > Papers by Mendelssohn (Fish Bull 1988) and DeValpine and Hilborn (CJFAS
> > 2005) pointed out problems with including latent states/missing data as
> > 'parameters' within maximum likelihood, but to my knowledge there hasn't
> > been much follow up with regard to typical parameters of interest
> > (abundance, biomass, etc.).  My sense is that MAP estimators still
> > perform reasonably well with moderate amounts of process error
> > (autocorrelated recruitment for instance) but it would be good to look
> > into further.
>
> > Paul
>
> > Saang-Yoon wrote:
> > > Dear ADMB users.
>
> > > I wonder about how people code multi-level models in ADMB.  I
> > > illustrate my question with a simple example.  Let's assume we have a
> > > simple regression model,
> > > Y = beta0 + beta1*X + error, where error ~ N(0, sigma2)
>
> > > Please think about two problems of (1) estimation of parameters
> > > (beta0, beta1, and sigma2), and then (2) prediction of unknown random
> > > variable (Y at a future time, given new X).  Strictly speaking,
> > > unknown Y at a future time (say, newY) is NOT a parameter but a random
> > > variable, although many fisheries papers treat the Y as a parameter.
> > > But I follow the incorrect treatment (i.e., newY as a parameter) at
> > > the moment to focus on my question about ADMB.  Also this is a simple
> > > “example” for showing my problem with ADMB when facing a hierarchical
> > > model.
>
> > > (1) Estimation of parameters, beta0, beta1, and sigma2
> > > L(beta0, beta1, sigma2 | observed Ys, observed Xs)
> > > This likelihood provides inference of these three parameters.  I call
> > > it L1
>
> > > (2) Calculation of new Y given new X.
> > > L(newY | beta0, beta1, sigma2, newX)
> > > I call this second likelihood function L2.  newX is a constant.
>
> > > These two steps can be viewed as a multi-level or hierarchical
> > > structure.  In ADMB, the objection function would be the sum of the
> > > respective negative loglikelihood functions: i.e.,
> > >  f = – logL1 – logL2;
> > > where beta0, beta1, sigma2, and newY are declared as free parameters
> > > in PARAMETER SECTION in ADMB.
>
> > > My problem with this above coding is that estimates of beta0, beta1,
> > > and sigma2 are affected by “newY” as well as “observed Ys” and
> > > “observed Xs”.  This is WRONG!!!   Estimation of beta0, and beta1, and
> > > sigma2 must depend ONLY on “observed Ys”, and “observed Xs”.
>
> > > I wonder about how ADMB experts do around this problem.  I would
> > > extremely appreciate your guidance and help.   Thank you,
>
> > > Saang-Yoon
> > > _______________________________________________
> > > Users mailing list
> > > Us... at admb-project.org
> > >http://lists.admb-project.org/mailman/listinfo/users
>
> > --
> > Paul B. Conn, Ph.D.
> > Research Statistician
> > National Marine Fisheries Service
> > NOAA Fisheries Center for Coastal Fisheries and Habitat Research
> > Southeast Fisheries Science Center
> > 101 Pivers Island Rd
> > Beaufort, NC 28516
> > phone252.838.0807begin_of_the_skype_highlighting              252.838.0807      end_of_the_skype_highlightingbegin_of_the_skype_highlighting              252.838.0807      end_of_the_skype_highlighting
> > fax 252.728.8619
> > Paul.C... at noaa.gov
>
> > "Information contained in this message does not represent the official
> > view of the National Oceanic and Atmospheric Administration."
>
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