1. Binary Regression

1.1. A Binary Regression Models

Consider a vector of independent dichotomous random variables, assuming that with probability and with probability , and a vector of covariates, where may equals , corresponding to an intercept, Moreover, denotes the design matrix with rows , and is a vector of regression coefficients. Binary regression models assume that where denotes a cumulative distribution function (cdf). The inverse function is typically called the link function and = is the linear predictor. Thus, a binary regression model is given is the linear predictor. Thus, a binary regression model is given by

When a cdf of a symmetric distribution, the response curve is has symmetric form about. Examples are obtained when is in the class of the elliptical distributions as, for example, standard normal, logistic, Student-, double exponential and Cauchy distributions.

In the case that is the cdf of a standard normal distribution we obtain the probit link

and in the case that is the cdf of a logistic distribution we obtain the logit link,

These links: probit and logit are implemented in BayesianModeling.