A0187
Title: BELIEF in dependence: Leveraging atomic linearity in data bits for rethinking generalized linear models
Authors: Kai Zhang - University of North Carolina at Chapel Hill (United States) [presenting]
Benjamin Brown - UNC Chapel Hill (United States)
Xiao-Li Meng - Harvard University (United States)
Abstract: Two linearly uncorrelated binary variables must also be independent because non-linear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, a framework called binary expansion linear effect (BELIEF) is developed for assessing and understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they describe the association of binary variables in the language of linear models, yielding convenient theoretical insight and striking parallels with the Gaussian world. In particular, an algebraic structure on the predictors with nonzero slopes governs conditional independence properties. With BELIEF, one may study generalized linear models (GLM) through transparent linear models, providing insight into how modelling is affected by choice of link. For example, setting a GLM interaction coefficient to zero does not necessarily lead to the kind of no-interaction model assumption understood under their linear model counterparts. These phenomena are explored, and a host of related theoretical results is provided. Preliminary empirical demonstration and verification of some theoretical results are also provided.
