Many thanks for sharing with us. On last graph of person fit, you mentioned that there were many misfit persons in this example dataset. Do we delete all the misfit persons? If so, the rest might to be too few to analyse. Or we just leave them in the analysis as long as ItemFit statistics are reasonable? Thanks!
A 'purist' would remove the persons, while a empirical investigator will leave them in the analysis and try to find out what made them misfits. I would go with the latter strategy and look into the data and the patterns of their answers to figure out the causes of being misfits. You would be surprised how much information you can obtain from the misfits!