MCMCpanel              package:MCMCpack              R Documentation

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

     MCMCpanel generates a sample from the posterior distribution of a
     General Linear Panel Model using Algorithm 2 of Chib and Carlin
     (1999). This model uses a multivariate Normal prior for the fixed
     effects parameters, a Wishart prior on the random effects
     precision matrix, and a Gamma prior on the conditional error
     precision. 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:

     MCMCpanel(obs, Y, X, W, burnin = 1000, mcmc = 10000, thin = 5, 
         verbose = 0, seed = NA, sigma2.start = NA,
         D.start = NA, b0 = 0, B0 = 1, eta0, R0, nu0 = 0.001,
         delta0 = 0.001, ...)
        

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

     obs: An (nk * 1) vector that contains unique observation numbers
          for each subject.

       Y: An (nk * 1) vector of response variables,  stacked across all
          subjects.

       X: An (nk * p) matrix of fixed effects covariates, stacked
          across all subjects.

       W: An (nk * q) matrix of random effects covariates, stacked
          across all subjects.

  burnin: The number of burnin iterations for the sampler.

    mcmc: The number of Gibbs iterations for the sampler.

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

    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.

 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 parameters are printed to the
          screen every 'verbose'th iteration.

sigma2.start: The starting value for the conditional error variance.
          Default value of NA uses the least squares estimates.

 D.start: The starting value for precision matrix of the random 
          effects.  This can either be a scalar or square matrix with
          dimension equal to the number of random effects. If this
          takes a scalar value, then that value multiplied by an
          identity matrix will be the starting value. Default value of
          NA uses an identity matrix multiplied by 0.5 the OLS sigma2
          estimate. 

      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.

    eta0: The shape parameter for the Wishart prior on precision matrix
          for the random effects.

      R0: The scale matrix for the Wishart prior on precision matrix
          for the random effects.

     nu0: The shape parameter for the Gamma prior on the conditional
          error precision.

  delta0: The scale  parameter for the Gamma prior on the conditional
          error precision.

     ...: further arguments to be passed

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

     'MCMCpanel' simulates from the posterior distribution sample using
      the blocked Gibbs sampler of Chib and Carlin (1999), Algorithm 2.
      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 + W_i * b_i + epsilon_i

     Where the random effects:

                            b_i ~ N_q(0,D)

     And the errors:

                    epsilon_i ~ N(0, sigma^2 I_k)

     We assume standard, conjugate priors:

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

     And:

                 sigma^(-2) ~  Gamma(nu0/2, delta0/2)

     And:

                     D^-1 ~ Wishart(eta0,  R0^-1)

     See Chib and Carlin (1999) or Martin and Saunders (2002) for more
     details.

     _NOTE: Unlike most models in MCMCpack, we do not provide default 
     parameters for the priors on the precision matrix for the random
     effects._ When fitting one of these models, it is of utmost
     importance to choose a  prior that reflects your prior beliefs
     about the random effects.  Using the 'dwish' and 'rwish' functions
     might be useful in choosing these values.  Also, the user is not
     allowed to specify a starting value for the beta parameters, as
     they are simulated in the first block of 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.

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

     Siddhartha Chib and Bradley P. Carlin. 1999. ``On MCMC Sampling in
      Hierarchical Longitudinal Models." _Statistics and Computing._ 9:
      17-26.

     Andrew D. Martin, Kevin M. Quinn, and Daniel Pemstein.  2004. 
     _Scythe  Statistical Library 1.0._ <URL: http://scythe.wustl.edu>.

     Andrew D. Martin and Kyle L. Saunders. 2002. ``Bayesian Inference
     for  Political Science Panel Data.'' Paper presented at the 2002
     Annual Meeting  of the American Political Science Association.

     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'

