Model fitting with ordinal logistic regression I am writing a research protocol which requires an ordinal logistic regression to be done (Kleinbaum and Klein, 2002). my outcome is type of neonatal admission with three levels, namely, NICU admission, High Risk admission, and Well Baby admission. My my predictors are number of antenatal care visits, age of gestation, birth weight, and two interaction terms number of visit x age of gestation and number of visit x birth weight.
From the literature that I searched, researchers used Hosmer-Lemeshow to test the model fit of logistic regression models but I wonder if it is also appropriate for ordered/ordinal logistic with a 3 level outcome? I will be using stata to run my tests.
 A: Spend your effort in well-specifying the model.  And note that Hosmer-Lemeshow is considered to be obsolete and does not directly apply to ordinal regression.  Besides carefully specifying the right-hand-side of the model (relaxing linearity assumptions through regression splines, pre-specifying interactions, etc.), assess the proportional odds model using tools such as partial residual plots with two cutoffs on $Y$.  Details are in my book Regression Modeling Strategies and my RMS course notes - see https://hbiostat.org/rms and https://hbiostat.org/bib/po.html
A: Yes, the Hosmer-Lemeshow test does extend to ordinal models. stata example of such implementation is discussed here.
For R users, there is a recent implementation of the ordinal Hosmer-Lemeshow test in the
gofcat package. The hosmerlem() function, in particular, returns results similar to those implemented in stata.
Another R implementation is from the generalhoslem package, however, with results different from stata implementation. The author's note in the package documentation says, "Finally, it has been observed that the results from this implementation of the binary and ordinal Hosmer-Lemeshow tests and the Lipsitz test are slightly different from the Stata implementations. It is not yet clear why this is but is under investigation."
