Ordinal Logistic Regression: A Model-free Approach

The binary logistic regression is a popular technique for classifying individuals into two mutually exclusive and exhaustive categories, namely, when the target variable is binary: for example, buy-not buy, or responder-non-responder. The ordinal logistic regression is the appropriate method when the target variable is ordinal, that is, there is a natural ordering of K (greater than 2) values of the target variable: for example, low, medium, and high. The ordinal logistic regression model is an assumption-full, parametric model in which the model structure (equation form) is pre-specified. The purpose of this article is to present the Genetic Ordinal Logistic Regression (GOLR) as an assumption-free, nonparametric model – model-free where the data defines the predictor variables and K-1 model equations – based on the machine learning paradigm of genetic programming. Pointedly, the ordinal logistic regression’s untenable assumption of parallel regression, i.e., there is only one set of coefficients across the K-1 equations, is a nonissue in GOLR. Moreover, the GOLR determines the best set of predictor variables based on a simultaneous and virtually unbiased assessment of all variables, an achievement not possible with the statistical ordinal logistic regression. GOLR is a straightforward extension of the GenIQ Model©, which serves as the model-free alternative to the binary logistic regression.

See companion article A Genetic Logistic Regression Model: A Model-free Approach to Identifying Responders to a CRM Solicitation