Dear Mark,<br><br>Here is a (partial) list of published paper discussing the methodology I am trying to implement. <br><div style="line-height: 1.1em; margin-left: 0.5in; text-indent: -0.5in;">
<p style="margin: 0pt;">------------------------------------------------------------------------------------------------------------------------------------------------<br></p><p style="margin: 0pt;">Brien, M. J., L. A. Lillard, and L. J. Waite. 1999. “Interrelated family-building behaviors: Cohabitation, marriage, and nonmarital conception.” <span style="font-style: italic;">Demography</span> 535-551. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Interrelated%20family-building%20behaviors%3A%20Cohabitation%2C%20marriage%2C%20and%20nonmarital%20conception&rft.jtitle=Demography&rft.aufirst=M.%20J.&rft.aulast=Brien&rft.au=M.%20J.%20Brien&rft.au=L.%20A.%20Lillard&rft.au=L.%20J.%20Waite&rft.date=1999&rft.pages=535-551"></span></p>
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<p style="margin: 0pt;">Lillard, L. A. 1993. “Simultaneous Equations for Hazards: Marriage Duration and Fertility Timing.” <span style="font-style: italic;">Journal of Econometrics</span> 56:189-217. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Simultaneous%20Equations%20for%20Hazards%3A%20Marriage%20Duration%20and%20Fertility%20Timing&rft.jtitle=Journal%20of%20Econometrics&rft.volume=56&rft.issue=1-2&rft.aufirst=L.%20A.&rft.aulast=Lillard&rft.au=L.%20A.%20Lillard&rft.date=1993&rft.pages=189-217"></span></p>
<p style="margin: 0pt;"><span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Simultaneous%20Equations%20for%20Hazards%3A%20Marriage%20Duration%20and%20Fertility%20Timing&rft.jtitle=Journal%20of%20Econometrics&rft.volume=56&rft.issue=1-2&rft.aufirst=L.%20A.&rft.aulast=Lillard&rft.au=L.%20A.%20Lillard&rft.date=1993&rft.pages=189-217"><br>
</span></p><p style="margin: 0pt;">Lillard, L. A., and L. J. Waite. 1993. “A joint model of marital childbearing and marital disruption.” <span style="font-style: italic;">Demography</span> 653-681. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A%20joint%20model%20of%20marital%20childbearing%20and%20marital%20disruption&rft.jtitle=Demography&rft.aufirst=L.%20A.&rft.aulast=Lillard&rft.au=L.%20A.%20Lillard&rft.au=L.%20J.%20Waite&rft.date=1993&rft.pages=653-681"><br>
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<br><p style="margin: 0pt;"><br></p><p style="margin: 0pt;">Steele, F., and S. L. Curtis. 2003. “Appropriate Methods for Analyzing the Effect of Method Choice on Contraceptive Discontinuation.” <span style="font-style: italic;">Demography</span> 40:1-22. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Appropriate%20Methods%20for%20Analyzing%20the%20Effect%20of%20Method%20Choice%20on%20Contraceptive%20Discontinuation&rft.jtitle=Demography&rft.volume=40&rft.issue=1&rft.aufirst=F.&rft.aulast=Steele&rft.au=F.%20Steele&rft.au=S.%20L.%20Curtis&rft.date=2003&rft.pages=1-22"><br>
</span></p><div style="line-height: 1.1em; margin-left: 0.5in; text-indent: -0.5in;">
</div><p style="margin: 0pt;"><br></p><p style="margin: 0pt;">Steele, F., C. Kallis, H. Goldstein, and H. Joshi. 2005. “The Relationship Between Childbearing and Transitions from Marriage and Cohabitation in Britain.” <span style="font-style: italic;">Demography</span> 42:647-673. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The%20Relationship%20Between%20Childbearing%20and%20Transitions%20from%20Marriage%20and%20Cohabitation%20in%20Britain&rft.jtitle=Demography&rft.volume=42&rft.issue=4&rft.aufirst=F.&rft.aulast=Steele&rft.au=F.%20Steele&rft.au=C.%20Kallis&rft.au=H.%20Goldstein&rft.au=H.%20Joshi&rft.date=2005&rft.pages=647-673"><br>
</span></p><div style="line-height: 1.1em; margin-left: 0.5in; text-indent: -0.5in;">
</div><p style="margin: 0pt;"><br></p><p style="margin: 0pt;">Upchurch, D. M., L. A. Lillard, and C. W. A. Panis. 2002. “Nonmarital childbearing: Influences of education, marriage, and fertility.” <span style="font-style: italic;">Demography</span> 311-329. <span class="Z3988" title="url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Nonmarital%20childbearing%3A%20Influences%20of%20education%2C%20marriage%2C%20and%20fertility&rft.jtitle=Demography&rft.aufirst=D.%20M.&rft.aulast=Upchurch&rft.au=D.%20M.%20Upchurch&rft.au=L.%20A.%20Lillard&rft.au=C.%20W.%20A.%20Panis&rft.date=2002&rft.pages=311-329"><br>
</span></p>
</div>------------------------------------------------------------------------------------------------------------------------------------------------<br>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. <br>
<br>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. <br>
<br>Thank you very much, and I am more than happy to contribute to the community in whatever way I can. <br><br>Best,<br>Shige<br><br><div class="gmail_quote">On Fri, Jun 5, 2009 at 12:54 PM, Mark Maunder <span dir="ltr"><<a href="mailto:mmaunder@iattc.org">mmaunder@iattc.org</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
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<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;">Shige,</span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;"> </span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;">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. </span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;"> </span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;">If you get the application working, I
would be interested in mentioning it in the ADMB newsletter (see <a href="http://admb-foundation.org/?page_id=39" target="_blank">http://admb-foundation.org/?page_id=39</a>).
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)</span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;"> </span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;">Regards,</span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;"> </span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;">Mark</span></font></p>
<p><font color="navy" face="Arial" size="2"><span style="font-size: 10pt; font-family: Arial; color: navy;"> </span></font></p>
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<p><b><font face="Tahoma" size="2"><span style="font-size: 10pt; font-family: Tahoma; font-weight: bold;">From:</span></font></b><font face="Tahoma" size="2"><span style="font-size: 10pt; font-family: Tahoma;">
<a href="mailto:users-bounces@admb-project.org" target="_blank">users-bounces@admb-project.org</a> [mailto:<a href="mailto:users-bounces@admb-project.org" target="_blank">users-bounces@admb-project.org</a>] <b><span style="font-weight: bold;">On Behalf Of </span></b>Shige Song<br>
<b><span style="font-weight: bold;">Sent:</span></b> Thursday, June 04, 2009 9:23
PM<br>
<b><span style="font-weight: bold;">To:</span></b> <a href="mailto:users@admb-project.org" target="_blank">users@admb-project.org</a><br>
<b><span style="font-weight: bold;">Subject:</span></b> Re: [ADMB Users] Examples
of multilevel multiprocess model</span></font></p>
</div><div><div></div><div class="h5">
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"> </span></font></p>
<p style="margin-bottom: 12pt;"><font face="Times New Roman" size="3"><span style="font-size: 12pt;">Dear Dave,<br>
<br>
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. <br>
<br>
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. <br>
<br>
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. <br>
<br>
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. <br>
<br>
My background is demography and sociology, some of the online examples do not
appear immediately intuitive to me. It has been an interesting experience. <br>
<br>
Best,<br>
Shige<br>
<br>
<br>
Maybe it will be more intuitive to begin with a well-know example. This (<a href="http://www.applied-ml.com/product/multiprocess.html" target="_blank">http://www.applied-ml.com/product/multiprocess.html</a>)
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</span></font></p>
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<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">On Thu, Jun 4, 2009 at 6:18 AM, dave fournier <<a href="mailto:otter@otter-rsch.com" target="_blank">otter@otter-rsch.com</a>>
wrote:</span></font></p>
<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;">It is not immediately obvious to me that ADMB can not handle a problem<br>
of this size. What I would need to know is the model structure.<br>
this is probably obvious to people who work with this kind of<br>
model every day. Please indulge me.<br>
<br>
If i indexes mothers and j indexes children I assum that for the 3<br>
outcomes we produce p_ijk where k=1,2,3 the three possible outcomes.<br>
and the P_ijk depend on a set of parameters including the random<br>
effects. If you could describe how the p_ijk are calculated I can give<br>
you better advice.<br>
<br>
Dave<br>
<font color="#888888"><span style="color: rgb(136, 136, 136);"><br>
<br>
<br>
<br>
--<br>
David A. Fournier<br>
P.O. Box 2040,<br>
Sidney, B.C. V8l 3S3<br>
Canada<br>
Phone/FAX 250-655-3364<br>
<a href="http://otter-rsch.com" target="_blank">http://otter-rsch.com</a></span></font></span></font></p>
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<p><font face="Times New Roman" size="3"><span style="font-size: 12pt;"> </span></font></p>
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