# [ADMB Users] Examples of multilevel multiprocess model

Shige Song shigesong at gmail.com
Thu Jun 4 21:23:05 PDT 2009

```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,

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
>
>   Dave
>
>
>
>
> --
> David A. Fournier
> P.O. Box 2040,
> Sidney, B.C. V8l 3S3
> Phone/FAX 250-655-3364
> http://otter-rsch.com
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