How to Fit Signal Detection Models as Bayesian Generalized Linear Models

Andrew Ellis

2019-03-27

Contents

Main points

GLM

The GLM generalizes a regression model by allowing the linear predictor to be related to the response variable via a link function.

We have to the following components:

Probit model

The most common model for binary responses is the logistic model. The probit model is related, but uses a different link function. The probit function is the quantile function associated with the normal distribution. The quantile function is also the inverse cumulative distribution function:

\[probit(x) = \Phi^{-1}(x) \]

and looks like this: