Supporting information S1 Text for Modeling genetic interactions using generalized linear models

A generalized linear model describes the distribution of random variable conditioned on one or more other random variables. The generalized linear model consists of two components: a distribution f(y) in the exponential family and a link function g that maps the linear predictor to the mean parameter of the distribution. Let yi for individual i ∈ {1...n} be the random variable that we want to model conditioned on a set of covariates xij for j ∈ {1...m}. Let X denote the matrix of covariates, and xi the vector of covariates corresponding to individual i. Vectors are denoted by bold face. The expected value of the outcome μi = E[Yi] for individual i is described as a function of the covariates g(μi) = xiβ = ηi, where we introduce ηi to simplify notation later. Because the distribution belongs to the exponential family, the likelihood of the model can be written on the following form