[ADMB Users] ADMB and hierarchical (multi-level) models
shyunuw at gmail.com
Tue Aug 17 16:35:10 PDT 2010
Yes, you are right if I have a stereotype of a hierarchical model
problem. There are variants of hierarchical models, and my example
is NOT the universal form where we estimate hyper parameters and main
parameters at the same level.
My example has mainly two components of (i) estimation of parameters
(e.g., newY) as the likelihood component and (ii) prediction (or
forecast) of unknown “RANDOM VARIABLE” (newY) as prior. The prior
predictive function has parameters that govern unknown newY. To avoid
the confusion, we may want to call those parameters differently from
hyper parameters. Anyhow, estimation of those parameters that govern
newY must be INDEPENDENT of the likelihood. However, when I implement
this example into ADMB, I find estimates of those parameters are
different from when being externally (independently) estimated. Again
the difference indicates the wrong calculation. To avoid this
problem, I could use MLEs (fixed values) for those parameters: i.e., I
put those MLEs as data values. In doing this later idea, some people
routinely criticize MLEs, saying those MLEs do not carry full
uncertainty in parameter estimates. I disagree with those routine
critiques about MLEs, but I do not talk about this new issue not to
distract from the original inquiry.
I greatly appreciate your interest in and comments about my inquiry.
On Aug 16, 7:42 pm, Saang-Yoon <shyu... at gmail.com> wrote:
> 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.
> 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
> > > > _______________________________________________
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> > > > 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 252.838.0807begin_of_the_skype_highlighting 252.838.0807 end_of_the_skype_highlighting 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
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> > > view of the National Oceanic and Atmospheric Administration."
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