[ADMB Users] Examples of multilevel multiprocess model

Shige Song shigesong at gmail.com
Thu Jun 4 22:58:05 PDT 2009

Dear Mark,

Here is a (partial) list of published paper discussing the methodology I am
trying to implement.


Brien, M. J., L. A. Lillard, and L. J. Waite. 1999. “Interrelated
family-building behaviors: Cohabitation, marriage, and nonmarital
conception.” Demography 535-551.

Lillard, L. A. 1993. “Simultaneous Equations for Hazards: Marriage Duration
and Fertility Timing.” Journal of Econometrics 56:189-217.

Lillard, L. A., and L. J. Waite. 1993. “A joint model of marital
childbearing and marital disruption.” Demography 653-681.

Steele, F., and S. L. Curtis. 2003. “Appropriate Methods for Analyzing the
Effect of Method Choice on Contraceptive Discontinuation.” Demography40:1-22.

Steele, F., C. Kallis, H. Goldstein, and H. Joshi. 2005. “The Relationship
Between Childbearing and Transitions from Marriage and Cohabitation in
Britain.” Demography 42:647-673.

Upchurch, D. M., L. A. Lillard, and C. W. A. Panis. 2002. “Nonmarital
childbearing: Influences of education, marriage, and fertility.”
Note that many of the models are more complicated that the one I have in
mind because they usually jointly model binary response, ordinal response,
and survival process, while what I am trying to do is to jointly model
several binary responses. I assume once I get the joint logistic model
working, it will be relatively straightforward to extend to handle the more
complicated cases.

As you will soon realized while reading through the article, all these
published works relied on the assumption of multivariate normality for the
unobserved heterogeneity terms, which has been increasingly questioned in
recent years.

Thank you very much, and I am more than happy to contribute to the community
in whatever way I can.


On Fri, Jun 5, 2009 at 12:54 PM, Mark Maunder <mmaunder at iattc.org> wrote:

>  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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