MCMClogit              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 _L_o_g_i_s_t_i_c _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 logistic
     regression model using a random walk Metropolis algorithm. 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:

     MCMClogit(formula, data = list(), burnin = 1000, mcmc = 10000,
        thin=5, tune=1.1, 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 Metropolis iterations for the sampler.

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

    tune: Metropolis tuning parameter.  Make sure that the acceptance
          rate is satisfactory before using the posterior density
          sample for inference.

 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 the maximum likelihood
          estimate of beta 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.

     ...: further arguments to be passed

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

     'MCMClogit' simulates from the posterior density of a logistic
     regression model using a random walk Metropolis algorithm. 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 ~ Bernoulli(pi_i)

     Where the inverse link function:

             pi_i =  exp(x_i'beta) / [1 + exp(x_i'beta)]

     We assume a multivariate Normal prior on beta:

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

     The candidate generating density is a multivariate Normal density
     centered at the current value of beta with variance-covariance
     matrix that is an approximation of the posterior based on the
     maximum likelihood  estimates and the prior precision multiplied
     by the tuning parameter   squared.

_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', 'glm'

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

        ## Not run: 
        data(birthwt)
        posterior <- MCMClogit(low~age+as.factor(race)+smoke, data=birthwt)
        plot(posterior)
        summary(posterior)
        
     ## End(Not run)

