Joint survival and logit model, selec...
Message/Author
 Shige Song posted on Saturday, July 28, 2007 - 1:36 am
Dear Linda and Bengt,

I am trying to study cohort variations of miscarriage and infant mortality in China. The model seems to be straightforward: miscarriage can be modeled using a logit/probit model while infant mortality can be modeled using a survival model (either discrete time or continuous time).

I have estimated the models separately and the results look all right. My concern is that the two processes, miscarriage and infant mortality, might not be independent and they are both influenced by some unobserved processes.

For example, it is not difficult to imagine that vulnerable fetuses are more likely to be subject for both miscarriage (before they are born) and immature death (after they are born). At time of famine, one would expect to see a sudden rise in both miscarriage rate and infant mortality rate. However, a rise in miscarriage rate may have negative impact on infant mortality rate because babies who are most vulnerable have not had a chance to be born. In other words, the impact of famine on infant mortality is likely to be underestimated because of the selectivity issue.

Do you have suggestions on how to tackle this issue? Thanks.

Best,
Shige
 Linda K. Muthen posted on Saturday, July 28, 2007 - 11:42 am
I see this as a single model where fetus/infant represent the unit of observation. The distinction about whether mortality occurred in or out of the uterus could be used as a covariate perhaps.
 Shige Song posted on Saturday, July 28, 2007 - 8:58 pm
Dear Linda,

I agree that fetus/infant should be the unit of observation. If whether mortality occurred out of the uterus is used as one of the covariates, what will be the dependent variable?

I have something like this in mind:

z=ax+u
y=bx+v

where z is a binary variable indicating whether a pregnancy ends up a live birth, and y is a continuous variable indicating time to event (death) .

Apparently, y is only observable when z takes the value of 1 (a pregnancy ends up with a live birth). Note that u and v are most likely to be positively correlated, which makes modeling each process separately undesirable.

I have two questions:
1) are there alternative approaches?
2) are there Mplus examples like this that I can borrow from?

Thanks.

Shige
 Shige Song posted on Sunday, July 29, 2007 - 7:52 am
I found this old post (http://www.statmodel.com/discussion/messages/11/740.html?1155563326), looks like I am not the only one trying to do this model using Mplus.

Shige
 Linda K. Muthen posted on Sunday, July 29, 2007 - 9:58 am
The dependent variable is time to death.

The model you propose is like a Heckman selection model where the second part is survival. This type of model cannot be estimated in Mplus.
 Shige Song posted on Monday, July 30, 2007 - 5:47 pm
I wonder if anyone has tried to implement the idea Bengt mentioned in the old post I quoted.

Shige
 Miranda Vervoort posted on Wednesday, September 29, 2010 - 4:57 am
Dear all,

I would like to estimate a Heckman selection model in Mplus. As I understand from these posts, that was not yet possible in 2007. But maybe new versions of Mplus does include possibilities to do a Heckman selection model? Can someone tell me about that?

Thank you very much,

Kind regards,
Miranda
 Bengt O. Muthen posted on Thursday, September 30, 2010 - 10:33 am
Tihomir and I talked about it and we think it is doable in Mplus, although it should be further explored. Both using ML and Bayes.

You have to score your continuous DV, say y, as missing when the binary DV, say u, indicates that it is not observed. With ML you cannot say y WITH u to get the residual covariance. So instead with ML you define a factor (F BY;) that you then let influence both y and u.

It seems like y and u need to have one covariate that is specific to them.