Built-in models:Logistic regression

Model

The logistic regression model with binary dependent variable \(y\) and independent variables \(\mathbf{x}=(x_{1},\ldots,x_{p})\) using a logit link,

\[y_{i} \sim Bernoulli(p_{i})\] \[logit(p_{i})=\log\left(\frac{p_{i} }{1-p_{i} }\right) = \beta_{0}+\beta_{1}x_{1i}+\ldots+\beta_{p}x_{pi}\]

In this model, the dependent variable can only take two values, 1 and 0. For example, in an experiment, 1 can represent success and 0 can represent failure. \(p_{i}\) is the probability that \(y_{i}=1\). Thus, \(p_{i}/(1-p_{i})\) is the odds that \(y_{i}=1\). Essentially, the predictors are predicting the log-odds.

Code

model{
  for (i in 1:N){
     y[i]~dbern(p[i])
     logit(p[i])<-beta0+beta1*(x1[i]-mean(x1[]))+beta2*(x2[i]-mean(x2[]))
  }
   beta0~dnorm(0,1.0E-6)
   beta1~dnorm(0,1.0E-6)
   beta2~dnorm(0,1.0E-6)
   exp1<-exp(beta1)
   exp2<-exp(beta2) 
}