Need Help for Sequential probit model

[Lubaba Binth Halim]

#urgent
#need_help
#sequential_probit

Hello everyone.

I am conducting a study on infant mortality. I need to use a sequential probit model. Let me specify: at the first step the outcome variable is whether the infant has died. y1=1 if dead 0 if alive. In the second step I see that given the infant has died what was the age of death, neonatal or post neonatal. So given y1= 1, if infant has died as neonatal y2=0 and if infant has died as post neonatal y2=1. These are the two steps of my sequential probit model. The explanatory variables in each stage are mostly similar but there are some differences. For simplicity let me say, vector of independent variable in the first step is X1 and in the second step X2.

Now, I don't know how to incorporate this model in stata. I don't know the necessary command or how to organise my dataset in stata. I am very much of a beginner in econometrics and do not possess much knowledge of stata.

Please someone help me in this regard. I kindly request you to be thorough in your answer so that I can understand.

What I know from theory is that in sequential probit model there is uncorrelated error terms and correlated error terms thing ( referring to correlation between error terms in two stages) . Now how to incorporate that to stata as estimation is likely to be different (?) in these two cases.

Another query: there could be some missing observations in my explanatory variable. will that be any problem?

Another query: as I said given that y1=1, I will see whether y2=neonatal phase death (0-1 month)=0 or y2=post neonatal phase death (1-12 month)=1, But there maybe some infants who died not within this periods, say in 24 months, So for them although y1=1, y2 wont take any value, it will be blank. Now would that be any problem for the model?

[Stephen Jenkins]

Is it essential to use probit? If you were to use sequential logit, there is seqlogit (SSC) written by Maarten Buis . His implementation doesn't address the correlated error terms issue. One can fit models with this feature using versions of multivariate probit models 'with selection'. On these, and indications of how to write the appropriate likelihood evaluator that can draw on available tools, see Cappellari & Jenkins, Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation, Stata Journal Stata Journal (2006) 6, Number 2, pp. 156–189. Getting convergence in sequential models can be tricky. You might also be able to adapt cmp (SSC) to fit such models but I haven't checked this functionality

[Maarten Buis]

My first thought was that the order of the stages is a bit weird: the first stage being dead or alive, and second stage being when you died. You don't first die and than decide at what age you died. Instead you just stay alive until you die. In other words you have a classic survival analysis problem, and since you dichotomized time to neonatal and post neonatal, you have a discrete time survival analysis. Here I will give this back to Stephen Jenkins He has useful material on how to estimate these models in Stata here: http://www.iser.essex.ac.uk/survival-analysis

It is no coincidence that we both answered this question, as what we do is very closely related: the sequential logit can be thought of as a special case of a discrete time survival model. However, since your problem is literally about babies surviving until a certain age, I think survival analysis is a more natural fit to your problem.

The problem of correlated error terms in survival models is typically referred to as frailty, and there is also a section on that on Stephen's website.

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