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


From   John Simpson <john.simpson@ualberta.ca>
To   statalist@hsphsun2.harvard.edu
Subject   st: Correct modeling procedure for a population growth model that includes extinction?
Date   Sat, 20 Feb 2010 09:55:21 -0700

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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