MCMCtobit              package:MCMCpack              R Documentation

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

     This function generates a sample from the posterior distribution 
     of a linear regression model with Gaussian errors using Gibbs
     sampling (with a multivariate Gaussian prior on the beta vector,
     and an inverse Gamma prior on the conditional error variance). 
     The dependent variable may be censored from below, from above, or
     both. 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:

     MCMCtobit(formula, data = parent.frame(), below = 0, above = Inf, 
       burnin = 1000, mcmc = 10000, thin = 1, verbose = 0, seed = NA, 
       beta.start = NA, b0 = 0, B0 = 0, c0 = 0.001, d0 = 0.001, ...)

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

 formula: A model formula.

    data: A dataframe.

   below: The point at which the dependent variable is  censored from
          below. The default is zero. To censor from  above only,
          specify that below = -Inf.

   above: The point at which the dependent variable is  censored from
          above. To censor from below only, use the default value of
          Inf.

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

    mcmc: The number of MCMC iterations after burnin.

    thin: The thinning interval used in the simulation.  The number of
          MCMC 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, the beta vector, and the error
          variance is 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 values for the beta vector. This can either be
          a scalar or a column vector with dimension equal to the 
          number of betas. The default value of of NA will use the OLS
          estimate of  beta as the starting value.  If this is a
          scalar, that value  will serve as the starting value mean for
          all of the betas.

      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
          for beta.

      c0: c0/2 is the shape parameter for the inverse Gamma prior on
          sigma^2 (the variance of the disturbances). The amount of
          information in the inverse Gamma prior is something like that
          from c0 pseudo-observations.

      d0: d0/2 is the scale parameter for the inverse Gamma prior on
          sigma^2 (the variance of the disturbances). In constructing
          the inverse Gamma prior, d0 acts like the sum of squared
          errors from the c0 pseudo-observations.

     ...: further arguments to be passed

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

     'MCMCtobit' simulates from the posterior distribution using
     standard Gibbs sampling (a multivariate Normal draw for the betas,
     and an inverse Gamma draw for the conditional error variance).
     'MCMCtobit' differs from 'MCMCregress' in that the dependent
     variable may be censored from below, from above, or both. 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 = x_i'beta + epsilon_i,

     where the errors are assumed to be Gaussian:

                      epsilon_i ~ N(0, sigma^2).

     Let c_1 and c_2 be the two censoring points, and let y_i^star be
     the partially observed dependent variable. Then,

               y_i = y_i^star if c_1 < y_i^star < c_2,


                    y_i = c_1 if c_1 >= y_i^star,


                    y_i = c_2 if c_1 <= y_i^star.

     We assume standard, semi-conjugate priors:

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

     and:

                   sigma^(-2) ~ Gamma(c0/2, d0/2),

     where beta and sigma^(-2) are assumed  _a priori_ independent. 
     Note that only starting values for beta are allowed because
     simulation is done using Gibbs sampling with the conditional error
     variance as the first block in the sampler.

_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.

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

     Ben Goodrich

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

     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/>.

     James Tobin. 1958. ``Estimation of relationships for limited
     dependent  variables." _Econometrica._, 26:24-36.

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

     'plot.mcmc', 'summary.mcmc',  'survreg', 'MCMCregress'

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

     ## Not run: 
     library(survival)
     example(tobin)
     summary(tfit)
     tfit.mcmc <- MCMCtobit(durable ~ age + quant, data=tobin, mcmc=30000,
                             verbose=1000)
     plot(tfit.mcmc)
     raftery.diag(tfit.mcmc)
     summary(tfit.mcmc)
     ## End(Not run)

