MCMChierEI             package:MCMCpack             R Documentation

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_I_n_f_e_r_e_n_c_e _M_o_d_e_l

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

     `MCMChierEI' is used to fit Wakefield's hierarchical ecological
     inference model for partially observed 2 x 2 contingency tables.

_U_s_a_g_e:

     MCMChierEI(r0, r1, c0, c1, burnin=1000, mcmc=50000, thin=1,
                m0=0, M0=10, m1=0, M1=10, nu0=1, delta0=0.5, nu1=1,
                delta1=0.5, verbose=FALSE, tune=2.65316, seed=0, ...)
        

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

      r0: (ntables * 1) vector of row sums from row 0.

      r1: (ntables * 1) vector of row sums from row 1.

      c0: (ntables * 1) vector of column sums from column 0.

      c1: (ntables * 1) vector of column sums from column 1.

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

    mcmc: The number of mcmc scans to be saved.

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

    tune: Tuning parameter for the Metropolis-Hasting sampling.

 verbose: A switch which determines whether or not the progress of the
          sampler is printed to the screen.  Information is printed if
          TRUE.

    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.

      m0: Prior mean of the mu0 parameter.

      M0: Prior variance of the mu0 parameter.

      m1: Prior mean of the mu1 parameter.

      M1: Prior variance of the mu1 parameter.

     nu0: Shape parameter for the inverse-gamma prior on the sigma^2_0
          parameter.

  delta0: Scale parameter for the inverse-gamma prior on the sigma^2_0
          parameter.

     nu1: Shape parameter for the inverse-gamma prior on the sigma^2_1
          parameter.

  delta1: Scale parameter for the inverse-gamma prior on the sigma^2_1
          parameter.

     ...: further arguments to be passed

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

     Consider the following partially observed 2 by 2 contingency table
     for unit t where t=1,...,ntables:


                  | Y=0      | Y=1      |
       - - - - -  - - - - -  - - - - -  - - - - -
       X=0        | Y0[t]    |          |r0[t]
       - - - - -  - - - - -  - - - - -  - - - - -
       X=1        | Y1[t]    |          | r1[t]
       - - - - -  - - - - -  - - - - -  - - - - -
                  | c0[t]    | c1[t]    | N[t]

     Where r0[t], r1[t], c0[t], c1[t], and N[t]  are non-negative
     integers that are observed. The interior cell entries are not
     observed. It is assumed that Y0[t]|r0[t] ~ Binomial(r0[t], p0[t])
     and  Y1[t]|r1[t] ~ Binomial(r1[t],p1[t]). Let theta0[t] =
     log(p0[t]/(1-p0[t])), and  theta1[t] = log(p1[t]/(1-p1[t])).

     The following prior distributions are assumed: theta0[t] ~
     Normal(mu0, sigma^2_0), theta1[t] ~ Normal(mu1, sigma^2_1).
     theta0[t] is assumed to be a priori independent of theta1[t] for
     all t. In addition, we assume the following hyperpriors: mu0 ~
     Normal(m0, M0), mu1 ~ Normal(m1, M1), sigma^2_0 ~ InvGamma(nu0/2,
     delta0/2), and sigma^2_1 ~ InvGamma(nu1/2, delta1/2).

     Inference centers on p0, p1, mu0, mu1, sigma^2_0, and sigma^2_1.
     The Metropolis-Hastings algorithm is used to sample from the
     posterior density.

_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:

     Jonathan Wakefield. 2001. ``Ecological Inference for 2 x 2
     Tables." Center for Statistics and the Social Sciences Working
     Paper no. 12. University of Washington. 

     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:

     'MCMCbaselineEI', 'MCMCdynamicEI', 'plot.mcmc','summary.mcmc'

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

        ## Not run: 
        c0 <- rpois(5, 500)
        c1 <- c(200, 140, 250, 190, 75)
        r0 <- rpois(5, 400)
        r1 <- (c0 + c1) - r0
        posterior <- MCMChierEI(r0,r1,c0,c1, mcmc=200000, thin=50)
        plot(posterior)
        summary(posterior) 
        
     ## End(Not run)

