Logic regression

Logic regression is an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates. In many regression problems a model is developed that relates the main effects (the predictors or transformations thereof) to the response, while interactions are usually kept simple (two- to three-way interactions at most). Often, especially when all predictors are binary, the interaction between many predictors may be what causes the differences in response. This issue arises, for example, in the analysis of SNP microarray data or in some data mining problems. In the proposed methodology, given a set of binary predictors we create new predictors such as "X-1, X-2, X-3, and X-4 are true," or "X-5 or X-6 but not X-7 are true." In more specific terms: we try to fit regression models of the form g(E[Y]) = b(0) + b(1)L(1) + (. . .) + b(n)L(n), where L-j is any Boolean expression of the predictors. The L-j and b(j) are estimated simultaneously using a simulated annealing algorithm. This article discusses how to fit logic regression models, how to carry out model selection for these models, and gives some examples.