MCMCoprobit             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 _O_r_d_e_r_e_d _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 an ordered probit regression model using the data augmentation 
     approach of Cowles (1996). 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:

     MCMCoprobit(formula, data = parent.frame(), burnin = 1000, mcmc = 10000,
        thin=1, tune = NA, verbose = 0, seed = NA, beta.start = NA,
        b0 = 0, B0 = 0, ...) 

_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 MCMC iterations for the sampler.

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

    tune: The tuning parameter for the Metropolis-Hastings step.
          Default of NA corresponds to a choice of 0.05 divided by the
          number of categories in the response variable.

 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, the beta vector, and the
          Metropolis-Hastings acceptance rate 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 rescaled estimates from an
          ordered logit model.

      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. 

     ...: further arguments to be passed

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

     'MCMCoprobit' simulates from the posterior distribution of a
     ordered 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 observed variable y_i is ordinal with a total of C 
     categories, with distribution governed by a latent variable:

                      z_i = x_i'beta + epsilon_i

     The errors are assumed to be from a standard Normal distribution. 
     The  probabilities of observing each outcome is governed by this
     latent variable and C-1 estimable cutpoints, which are denoted
     gamma_c.  The probability that individual i is in category c is
     computed by:

    pi_ic = Phi(gamma_c - x_i'beta) - Phi(gamma_(c-1) - x_i'beta)

     These probabilities are used to form the multinomial distribution
     that defines the likelihoods.

     The algorithm employed is discussed in depth by Cowles (1996). 
     Note that  the model does include a constant in the data matrix. 
     Thus, the first element  gamma_1 is normalized to zero, and is not
      returned in the mcmc object.

_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:

     M. K. Cowles. 1996. ``Accelerating Monte Carlo Markov Chain
     Convergence for Cumulative-link Generalized Linear Models."
     _Statistics and Computing._ 6: 101-110.

     Valen E. Johnson and James H. Albert. 1999. ``Ordinal Data
     Modeling."  Springer: New York.

     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'

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

        ## Not run: 
        x1 <- rnorm(100); x2 <- rnorm(100);
        z <- 1.0 + x1*0.1 - x2*0.5 + rnorm(100);
        y <- z; y[z < 0] <- 0; y[z >= 0 & z < 1] <- 1;
        y[z >= 1 & z < 1.5] <- 2; y[z >= 1.5] <- 3;
        posterior <- MCMCoprobit(y ~ x1 + x2, tune=0.3, mcmc=20000)
        plot(posterior)
        summary(posterior)
        
     ## End(Not run)

