A Note on Ordinal Modeling of Smoking Rate Data

This paper discusses statistical models for ordinal data that may be more appropriate for smoking rate outcomes than are models that assume continuous measurement and normality. Smoking rate outcomes often have distributions that make them inappropriate for many popular statistical models that assume normality, and are more appropriately considered ordinal outcomes. This article describes how the ordinal logistic regression model can be used to obtain estimates of means, and comparisons of means, for smoking rate outcomes.

Analyses of the daily smoking rate of a sample of 383 subjects are presented using linear regression and ordinal logistic regression. From the latter, we derive regression estimates (intercepts and slopes) in terms of the mean response without having to assume any distributional form for the smoking rate outcome variable. Regressors considered are the subject's gender and their level of dependency as assessed by the nicotine dependence symptom scale.

Estimated regression coefficients were similar, but the linear regression model indicated a significant gender effect, such that females had a higher smoking rate than males. Though similar, this effect was not quite significant (at the 0.05 level) in the ordinal model. The effect of dependency was significant in both models, with more dependent smokers having a higher smoking rate.

Results and conclusions can depend on the assumptions of a statistical model. Methods relaxing the assumption of normality are useful to examine how robust effects are to this common assumption.