Hi Dr. Asparouhov & Muthen, I am reading your paper " Multilevel modeling of complex survey data" (2006). On page 2724, while doing simulation, you gave us two formulas of selection probability for individual level and cluster level respectively (formula 12, and formula 14). I wonder how you got them.
This is specific for the simulation study and it is how we introduce the unequal probability sampling at the two-levels during the data generation process. You can choose different formulas and should expect similar results. The probability of selection depends on the observed variables. If they don't then the weights are non-informative and can be ignored. You can see more about informative v.s. non-informative weights here http://www.statmodel.com/download/JSM2007000745.pdf