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Evaluation of Proportional Odds and Continuation Ratio Models for Smoker in Indonesia

The polytomous model is a model used for more than two categorical response data. Some models that can use for ordinal scale responses are the Proportional Odds Model, Continuation Model, Partial Proportional Odds Model, and Adjacent Model. The Proportional Odds model has the assumption of "proportionality" or parallelity to the cumulative logit. If the parallel logits assumption not fulfilled, the alternative models that can use are Adjacent Model and Continuation-Ratio. The purpose of this study is to evaluate the proportional Odds (PO) model and Continuation-Ratio (CR) for smokers in Indonesia. The data used was taken from 2017 Indonesian Demographic and Health Survey (IDHS) by classifying smokers in ordinal categories (mild, moderate, and severe). The results show there was a violation of the assumptions in the PO Model so that the CR Model was an alternative to use. Gender is a factor that has a significant influence on all response categories. Based on the value of Goodness of fit, deviance, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Mac Fadden R2 indicate that the CR Model is better to use than the Model PO.