Summary
I have tried to indicate not only the analytic differences in some of the points made in the paper and the rejoinder, but also the perspective from which these differences arise. The point of the paper, and these remarks, is to show how the special case of the MPM revealed why the joining assumption and dichotomization are not, in general, properties of the URM for graded responses, and, thereby to identify the circumstances where one would require that this property did not hold in empirical graded responses.
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Andrich, D. Further remarks on nondichotomization of graded responses. Psychometrika 60, 37–46 (1995). https://doi.org/10.1007/BF02294428
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DOI: https://doi.org/10.1007/BF02294428