Abstract
Questionnaires with uniform-ordered categorical response formats are widely applied in psychology. Muraki proposed a modified graded response model accounting for the items' uniform response formats by assuming identical threshold parameters defining the category boundaries for all items. What is not well known is that there is a set of closely related models, which similarly assume identical thresholds. The present article gives a framework illustrating the differences between these models and their utility for understanding questionnaire responses in detail. The models are explained as constrained cases of a one-dimensional factor model for ordered categorical data. Furthermore, the authors show that the models can be written and fitted as structural equation models, which allows for a very flexible and general purpose use. Instructions on implementing the models in Mplus and SAS PROC NLMIXED are given.
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