I have data coming from a sample that, for various reasons, don't follow the original sampling plan. Trying to calibrate this sample seems to be very difficult because deviations are hard in some cases.
At first the design aimed to include a number of small regions but not all of them have participated in the study. If we consider bigger areas we have data from all of them but the distribution in the sample is very different from the population (even for post-calibration techniques).
As we have a large amount of data, would it be a good solution to draw a random subsample from this dataset following the probabilities observed in the population by different characteristics?