have the following logistic regression problem I am trying to solve using bayesian approach.

" We consider a logistic regression setting where the objective is to model Pij, the probability of an occurence for the jth individual in the ith group,i = 1, 2, ....I, j = 1, 2, ...J. We assume log (Pij/1-Pij) = beta0 + beta1*Xi + beta2*Zij and seek inference regarding beta1, the coefficient of the population level covariate and beta2, the coefficient of the individual level covariate. In particular we set I =2 and let Xi = 01, indicating which of the two groups was sampled

Zij = U(0,1)

Priors: beta0 = N(0,10), beta1 = U(1,1.5), beta2 = U(1,2) "

Questions:

1. I am not really sure of the use of variable Xi in the model? Is this a standard way of writing a logistic regression model? Some references would be useful.

2. Given the priors, can I use R to code (Gibbs sampler with adaptive rejective sampling - have to use this) this problem? Are there any standard R packages available to do this? Some pointers would be helpful.

Thanks a lot.