[ADMB Users] ADMB and hierarchical (multi-level) models
shyunuw at gmail.com
Mon Aug 16 16:33:23 PDT 2010
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,
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.
> 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
> > _______________________________________________
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> > Us... at admb-project.org
> 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
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