MCMCregress             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 _G_a_u_s_s_i_a_n _L_i_n_e_a_r _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 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 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:

     MCMCregress(formula, data = list(), burnin = 1000, mcmc = 10000,
        thin = 5, verbose = FALSE, seed = 0, sigma2.start = NA,
        b0 = 0, B0 = 0, nu = 0.001, delta = 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 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, the beta vector, and the conditional error variance
          is 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.

sigma2.start: The starting value for the conditional error variance.
          The default value of of NA will use the maximum likelihood
          estimate of sigma2 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
          for beta.

      nu: nu/2 is the shape parameter for inverse-Gamma prior  on the
          conditional error  variance.

   delta: delta/2 is the scale parameter for  inverse-Gamma prior on
          the conditional error variance.

     ...: further arguments to be passed

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

     'MCMCregress' simulates from the posterior density using  standard
     Gibbs sampling (a multivariate Normal draw for the betas, and an
     inverse-Gamma draw for the conditional error variance).  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 = x_i'beta + epsilon_i

     Where the errors are assumed to be Gaussian:

                      epsilon_i ~ N(0, sigma^2)

     We assume standard, conjugate priors:

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

     And:

                  sigma^(-2) ~ Gamma(nu/2, delta/2)

     Where beta and sigma^(-2) are assumed  _a priori_ independent. 
     Note that only starting values for the conditional error variance
     are allowed because beta is the first block in the sampler.

_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:

     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', 'lm'

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

        ## Not run: 
        line   <- list(X = c(1,2,3,4,5), Y = c(1,3,3,3,5))
        line$X <- line$X - mean(line$X)
        posterior  <- MCMCregress(Y~X, data=line)
        plot(posterior)
        summary(posterior)
        
     ## End(Not run)

