[ADMB Users] Examples of multilevel multiprocess model
Mark Maunder
mmaunder at iattc.org
Thu Jun 4 21:54:02 PDT 2009
Shige,
I have been glancing over your posts and the replies. ADMB should be
able to handle your model with non Gaussian random effects and probably
nonparametric random effects as well. Dave or Hans could probably code
the model in ten minutes, the rest of us would take longer. I suggest
that you send the exact equations that you want to use (or point us to a
published paper that has them) to make it easier to understand.
If you get the application working, I would be interested in mentioning
it in the ADMB newsletter (see http://admb-foundation.org/?page_id=39).
I am trying to highlight non-fisheries applications in the newsletter to
promote ADMB to non-fisheries scientists. (anyone else out there with a
non-fisheries application let me know as well)
Regards,
Mark
________________________________
From: users-bounces at admb-project.org
[mailto:users-bounces at admb-project.org] On Behalf Of Shige Song
Sent: Thursday, June 04, 2009 9:23 PM
To: users at admb-project.org
Subject: Re: [ADMB Users] Examples of multilevel multiprocess model
Dear Dave,
What I have in mind is really two sets of models. First of all, I want
to estimate three random intercept logistic regression models. Second, I
want to jointly estimate the three models together, allowing the random
effects in the three models to be freely correlated.
The first step is simple and can be done in many statistical packages
(such as Stata, R, MLwiN, HLM, aML, etc.) as well as ADMB. Although the
default of most estimation procedures uses univariate Gaussian
distribution, it is possible to estimate the random effect using
non-parametric maximum likelihood using some of these packages (GLLAMM,
R, aML). In that sense, it is quite easy to check the Gaussian
distributional assumption: just estimate a model assuming Gaussian
random effect and a model with non-parametric random effect, then
compare the two models. It is also quite easy to estimate random effect
model assuming other distributions (e.g. log-normal, student t) using
ADMB, as demonstrated in the ADMB-RE manual.
Such possibles do not seem to exist when one tries to estimate joint
models (also known as "multivariate model" or "multiprocess model").
Jointly modeling three random intercept logistic regressions improves
efficiency; also, the joint model yields two addiitonal parameters: the
correlaiton between the three random effects (or the two covariance
terms if parameterized as variance/covariance matrix). These two
correlation coefficients happen to be important to my research.
Now I know that aML and Sabre can handle joint models as such, assuming
the random effects to be multivariate Gaussian. No software seem to be
able to handle multivariate random effects non-parametrically yet
(through multivariate non-parametric maximum likelihood, although the
Sabre team seems to be working on it). ADMB and WinBUGS seem to be able
to estimate the joint models under alternative parametric assumptions
for the multivariate random effects. From what I read, WinBUGS can be
very slow (especially when there are more than 100,000 observations).
Since both are new to me, it makes most sense to spend time on the one
that can handle my problem.
My background is demography and sociology, some of the online examples
do not appear immediately intuitive to me. It has been an interesting
experience.
Best,
Shige
Maybe it will be more intuitive to begin with a well-know example. This
(http://www.applied-ml.com/product/multiprocess.html) is an aML
implementation of the single-level Heckman selection model that jointly
model a continuous outcome and a binary outcome. Very little
modification is needed to extend it to a multilevel situation
On Thu, Jun 4, 2009 at 6:18 AM, dave fournier <otter at otter-rsch.com>
wrote:
It is not immediately obvious to me that ADMB can not handle a problem
of this size. What I would need to know is the model structure.
this is probably obvious to people who work with this kind of
model every day. Please indulge me.
If i indexes mothers and j indexes children I assum that for the 3
outcomes we produce p_ijk where k=1,2,3 the three possible outcomes.
and the P_ijk depend on a set of parameters including the random
effects. If you could describe how the p_ijk are calculated I can give
you better advice.
Dave
--
David A. Fournier
P.O. Box 2040,
Sidney, B.C. V8l 3S3
Canada
Phone/FAX 250-655-3364
http://otter-rsch.com
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