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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. Thank you in advance.

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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 links at http://www.fharrell.com/p/blog-page.html

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