st: Correct modeling procedure for a population growth model that includes extinction?

[John Simpson <john.simpson@ualberta.ca>]

I have a set of panel data produced through simulation that features  
populations of artificial beings or agents.  Each simulation proceeds  
by randomly generating a population of unique individuals and then  
allowing the members of the population to interact with each other.   
The size of the population is the result of the interaction of the  
individuals within the population and the environmental conditions  
that are set at the creation of each population and then remain  
constant throughout.  Each population is simulated for 100 generations  
and population size is sampled at regular intervals for each  
population that is simulated.

I am interested in building a model that can provide a population  
growth curve over the range of environmental conditions covered in the  
samples.

The problem is that not every population survive through the entire  
period; populations go extinct with increasing frequency as the  
harshness of the environmental conditions are increased.  This creates  
an unbalanced dataset and I am not sure how to handle this result  
without biasing the results.

1. Since the population sizes are not missing at random (MAR) it seems  
that xtmixed may not be appropriate.  This missing data can be  
overcome using tsfill and carryforward, but I worry that this will  
unduly bias the results.

2. Since there are mixed effects it seems that xttobit may not be  
appropriate even though it allows for the treatment of truncated and  
censored data.

Any suggestions on how to proceed would be appreciated.  Any direction  
towards relevant literature or research would also be appreciated.
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