I have panel data: individuals and years. Individuals can self-select in two different treatments. After the self-selection, there is a randomization and only some individuals eventually get the treatment. To compare the two treatments, I would like to use an inverse probability of treatment weights. I plan to use a multinomial probit model to predict the probability of self-selection in the treatment, and then predict the iptw. Does it look right? Any suggestions?
It seems you have 4 groups: wanted A and got A, wanted A and got nothing, wanted B and got B, wanted B and got nothing. I presume you want to know the causal effect of A vs. B, so those that got nothing are not really relevant to the causal estimand (and can be combined into one group).
Multinomial probit (or logit) can be used to estimate the propensity scores and then you can weight by the inverse of the predicted probability of being in the treatment that was received. Make sure to assess whether weighting actually achieved balance on your covariates. You might think about using generalized boosted modeling or covariate balancing propensity scores to improve the quality of your weights.