BLogit                package:Baldur                R Documentation

_B_a_y_e_s_i_a_n _l_o_g_i_t _m_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     'BLogit' produces iid draws from the posterior density of a
     Bayesian Logit model with a multivariate normal prior.

_U_s_a_g_e:

     BLogit(y,X,alpha,mu,P,draws,Prec=FALSE,A=FALSE)

_A_r_g_u_m_e_n_t_s:

       y: n*2 Matrix with counts for the two categories.  

       X: n*k Matrix with the values for the independent variables.

   alpha: constant vector added to X*beta.

      mu: k*1 Prior mean vector.

       P: k*k Prior variance-covariance matrix (must be Positive
          Definite). If Prec=TRUE,  this is instead treated as the
          prior precision matrix (inverse variance-covariance matrix).

   draws: Numeric variable containing number of desired draws from the
          posterior density. Non-integer values are rounded to the
          nearest integer.

    Prec: Optional logical argument with default Prec=FALSE.  If
          argument is set to TRUE,  the matrix P is treated as a prior
          precision matrix.

       A: Optional logical argument with default A=FALSE.  If argument
          is set to TRUE,  the function returns not only the simulated
          draws from the posterior density but also a vector with
          information  related to the acceptance rate for the
          underlying accept/reject procedure (see below).

_D_e_t_a_i_l_s:

     Makes use of the likelihood subgradient density accept/reject
     procedure of Nygren and Nygren (2006) in order to generate iid
     samples from the posterior density of a Bayesian Logit model with
     a multivariate normal prior. If the posterior density is close to
     multivariate normal, then the expected number of draws should be
     approximately equal to $(2/sqrt{pi})^{k}$.

_V_a_l_u_e:

     If A=FALSE, a matrix beta. If A=TRUE, a list containing the matrix
     beta and a matrix Accept.: 

   beta : draws*k matrix with the iid draws for the model parameters.

  Accept: draws*1 matrix with the number of candidates for each draw
          that were required before acceptance in the accept/reject
          procedure.

_A_u_t_h_o_r(_s):

     Kjell Nygren knygren@us.imshealth.com

_R_e_f_e_r_e_n_c_e_s:

     Nygren and Nygren (2006) Likelihood Subgradient Densities.
     Upcoming \textit{Journal of American Statistical Association}

_E_x_a_m_p_l_e_s:

                   

     # Bayesian Logit Model for Crowders Seed Data 

     # Step 1: Read in and setup data for BLogit Function

     data( Seeds,package = "Baldur")

     y<-as.matrix(Seeds[,2:3])

     X<-as.matrix(Seeds[,4:7])

     mu<-matrix(0,nrow=4,ncol=1)
     alpha<-matrix(0,nrow=21,ncol=1)
     P<-100*diag(4)
     draws<-1000

     # Step 2: Set random number seed and run simulation for Bayesian Logit Model

     set.seed(666)
     system.time(sim<-BLogit(y,X,alpha,mu,P,draws))

