The Probit Link Function in Generalized Linear Models for Data Mining Applications

The use of logistic regression for outcome classification of dichotomous variables is well known in data mining applications. The estimated probability of the logit transformation belongs to the class of canonical link functions that follow from particular probability distribution functions. A closely related model is the probit link which can be used for binary responses. Although the probit link is not canonical, in some cases the overall fit of the model can be improved by using non-canonical link functions. This article reviews the properties of the probit link function and discusses its applications in data mining problems. Contrasts and comparisons are made with the logistic link function and an example provides further illustration. Introduction The problem of outcome classification of qualitative data is a major task in data mining. The goal of classification is to accurately predict the target class for each case in the data. Specifically, in binary classification, the target attribute has only two possible outcomes and fast and accurate classifiers are highly desirable. Several predictive models such as naïve Bayes, classification trees, support vector machine and k-nearest neighbor have traditionally been used with some success. However, recently the use of logistic regression has found more widespread popularity and the method has attracted the attention of several practitioners. The advantage of such a model is that it transforms information about the binary dependent variable into an