I am interested in determining if the decisionmaking of a particular government body was responsive to policy and statutory changes that occurred at known points in time.
I can classify the decisions of this body as 1) rejected proposal; 2) accepted modified proposal; 3) accepted proposal (without change).
I could classify the policy or statutory changes dichotomously -- "with deregulation" and "without deregulation," for example.
The intervention model discussed in this previous question - "Quantifying effect of a categorical variable in time series analysis" - seems highly relevant, but I think there are important differences between my dataset and the dataset described there:
In the linked question, the OP had a continuous response variable. In my case, I could take the categorical "decision" variable and convert it to a continuous "rate accepted" or "rate rejected" variable, BUT
The timing of the response variable may not be as easily coded. There is a lag between the time at which a decision was requested from the government body and the time at which the body made this decision, and this lag varies considerably from observation to observation. Further, decisions generally occur in bunches (a phenomenon I can't readily explain) -- that is, a scheme of intervals used to measure "rate accepted" would have considerable variation in N from interval to interval.
In general, I'm interested in whether there's a modification to the intervention model described in the link above that I should investigate, or any other model that might be relevant? A colleague suggested ARIMAX, of which I know nothing.