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 posterior density sample from 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 density 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 = list(), burnin = 1000, mcmc = 10000,
        thin=5, tune = NA, verbose = FALSE, seed = 0, beta.start = NA,
        b0 = 0, B0 = 0.001, ...) 

_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 TRUE, the iteration
          number and the betas are printed to the screen every 500
          iterations.

    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 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.

     ...: further arguments to be passed

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

     'MCMCoprobit' simulates from the posterior density 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 density
     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 density 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.  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'

_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)

