Logistic probability mbdels-models linear in the log odds of the outcome event-have found extensive application in modelling of unordered categorical responses. This paper illustrates some extensions of logistic models to the modelling of probabilities of ordinal responses. The extensions arise naturally from discrete probability models for the conditional distribution of the ordinal response, as well as from linear modelling of the log odds of response. Methods of estimation and examination of fit developed for the binary logistic model extend in a straightforward manner to the ordinal models. The models and methods are illustrated in an analysis of the dependence of chronic obstructive respiratory disease prevalence on smoking and age.
K e y words
: Biometry ; epidemiologic methods; odds ratio ; statistics An Application of Logistic Models to the Analysis of Ordinal Responses
In the study of the dependence of a response (outcome) variable on one or more independent variables, the method or model of choice is largely determined by the scale of measurement of the response variable. The scale of response may be one of three major types (1,2) : 1) nominal (or qualitative), which involves no ordering of the response values (e.g., cause of death-cancer, heart disease, etc..) ; 2 ) ordinal, which involves only ranking of the response values without any specified distance between the values (e.g., clinical diagnostic category-clinically manifest disease, preclinical disease, disease absent) ; and 3) interval (including continuous response), which involves both ranking of values and distance between values (e.g., systolic blood pressure as measured in terms of mm Hg).
Regression and analysis-of-variance methods for nominal and interval responses have been widely disseminated (2-6), but parametric models for the analysis of ordinal responses have received much less development. As a result, it is common