I have estimated an order logit model: I have one utility function (without constant, in the form $\sum_i \beta_i * x_i$) with cuts and I estimated the $\beta_i$ and the cuts on revealed preference data (sample of the population).
I would like now to apply this model on two synthetic populations that I have, one for today and one for the future. For each individual in the synthetic population, I compute the probability of each possible output (0, 1, 2, …, 6).
Problem: In the revealed preference data, the dependent variable is on average 0.6, while in the synthetic population (today version), the average of the output of the model is 0.3.
In standard logit models, it is recommended to recalibrate the alternative speciﬁc constants against observed market shares (see e.g. Discrete Choice Methods with Simulation, by Kenneth Train, chapter 2.8, page 33). In my particular case, there is no constant, but I was thinking of including a constant in the utility function in order to correct for the different nature of the data for estimation (revealed preference data) and simulation/forecasting (synthetic population).
Does this approach make sense to you? Has anyone done such a process in the scientific literature? I have found nothing till now.
In any case, I need to make a correction in order to reproduce the aggregate observation of 0.6, before being able to use my model for forecasting. If you have any other strategy than including a constant, I would be very interested.