A goodness-of-fit test for the ordered stereotype model.

This paper presents a new goodness-of-fit test for an ordered stereotype model used for an ordinal response variable. The proposed test is based on the well-known Hosmer-Lemeshow test and its version for the proportional odds regression model. The latter test statistic is calculated from a grouping scheme assuming that the levels of the ordinal response are equally spaced which might be not true. One of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories, dictated by the data. The proposed test takes the use of this new adjusted spacing to partition data. A simulation study shows good performance of the proposed test under a variety of scenarios. Finally, the results of the application in two examples are presented.