MCMCprobit             package:MCMCpack             R Documentation

_M_a_r_k_o_v _c_h_a_i_n _M_o_n_t_e _C_a_r_l_o _f_o_r _P_r_o_b_i_t _R_e_g_r_e_s_s_i_o_n

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

     This function generates a posterior density sample from a probit
     regression model using the data augmentation approach of Albert
     and Chib (1993). The user supplies data and priors, and a sample
     from the posterior density is returned as an mcmc object, which
     can be subsequently analyzed with functions  provided in the coda
     package.

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

     MCMCprobit(formula, data = list(), burnin = 1000, mcmc = 10000,
        thin = 5, verbose = FALSE, seed = 0, beta.start = NA,
        b0 = 0, B0 = 0, bayes.resid = FALSE, ...) 

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

 formula: Model formula.

    data: Data frame.

  burnin: The number of burn-in iterations for the sampler.

    mcmc: The number of Gibbs iterations for the sampler.

    thin: The thinning interval used in the simulation.  The number of
          Gibbs iterations must be divisible by this value.

 verbose: A switch which determines whether or not the progress of the
          sampler is printed to the screen.  If TRUE, the iteration
          number and the betas are printed to the screen.

    seed: The seed for the random number generator.  The code uses the
          Mersenne Twister, which requires an integer as an input.  If
          nothing is provided, the Scythe default seed is used.

beta.start: The starting value for the beta vector.     This can either
           be a scalar or a column vector with dimension equal to the
          number of  betas.  If this takes a scalar value, then that
          value will serve as  the  starting value for all of the
          betas. The default value of NA will use the maximum
          likelihood estimate of beta as the starting  value.

      b0: The prior mean of beta.  This can either be a  scalar or a
          column        vector with dimension equal to the number of
          betas. If this takes a scalar value, then that value will
          serve as the prior mean for all of the betas.

      B0: The prior precision of beta.  This can either be a     
          scalar or a square matrix with dimensions equal to the number
          of betas.  If this takes a scalar value, then that value
          times an identity matrix serves as the prior precision of
          beta. Default value of 0 is  equivalent to an improper
          uniform prior on beta.

bayes.resid: Should latent Bayesian residuals (Albert and Chib, 1995)
          be returned? Default is FALSE meaning no residuals should be
          returned. Alternatively, the user can specify an array of
          integers giving the observation numbers for which latent
          residuals should be calculated and returned. TRUE will return
          draws of latent residuals for all observations.

     ...: further arguments to be passed

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

     'MCMCprobit' simulates from the posterior density of a probit
     regression model using data augmentation. The simulation proper is
     done in compiled C++ code to maximize efficiency.  Please consult
     the coda documentation for a comprehensive list of functions that
     can be used to analyze the posterior density sample.

     The model takes the following form:

                        y_i ~ Bernoulli(pi_i)

     Where the inverse link function:

                         pi_i = Phi(x_i'beta)

     We assume a multivariate Normal prior on beta:

                         beta ~ N(b0,B0^(-1))

     See Albert and Chib (1993) for estimation details.

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

     An mcmc object that contains the posterior density sample.  This 
     object can be summarized by functions provided by the coda
     package.

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

     Albert, J. H. and S. Chib. 1993. ``Bayesian Analysis of Binary and
     Polychotomous Response Data.'' _J. Amer. Statist. Assoc._ 88,
     669-679

     Albert, J. H. and S. Chib. 1995. ``Bayesian Residual Analysis for
     Binary Response Regression Models.'' _Biometrika._ 82, 747-759.

     Andrew D. Martin, Kevin M. Quinn, and Daniel Pemstein.  2003.  
     _Scythe Statistical Library 0.4._ <URL: http://scythe.wustl.edu>.

     Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2002.
     _Output Analysis and Diagnostics for MCMC (CODA)_. <URL:
     http://www-fis.iarc.fr/coda/>.

_S_e_e _A_l_s_o:

     'plot.mcmc','summary.mcmc', 'glm'

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

        ## Not run: 
        data(birthwt)
        posterior <- MCMCprobit(low~age+as.factor(race)+smoke, data=birthwt)
        plot(posterior)
        summary(posterior)
        
     ## End(Not run)

