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 sample from the posterior distribution
     of 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 distribution 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 = parent.frame(), burnin = 1000, mcmc = 10000,
        thin = 1, verbose = 0, seed = NA, beta.start = NA,
        b0 = 0, B0 = 0, bayes.resid = FALSE,
        marginal.likelihood=c("none", "Laplace"), ...) 

_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 'verbose' is greater
          than 0 the iteration number and the betas are printed to the
          screen every 'verbose'th iteration.

    seed: The seed for the random number generator.  If NA, the
          Mersenne Twister generator is used with default seed 12345;
          if an integer is  passed it is used to seed the Mersenne
          twister.  The user can also pass a list of length two to use
          the L'Ecuyer random number generator, which is suitable for
          parallel computation.  The first element of the list is the
          L'Ecuyer seed, which is a vector of length six or NA (if NA 
          a default seed of 'rep(12345,6)' is used).  The second
          element of  list is a positive substream number. See the
          MCMCpack  specification for more details.

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.

marginal.likelihood: How should the marginal likelihood be calculated?
          Options are: 'none' in which case the marginal likelihood
          will not be calculated or 'Laplace' in which case the Laplace
          approximation (see Kass and Raftery, 1995) is used.

     ...: further arguments to be passed

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

     'MCMCprobit' simulates from the posterior distribution 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 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 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.  2004.  
     _Scythe Statistical Library 1.0._ <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)

