bayessurvreg1           package:bayesSurv           R Documentation

_A _B_a_y_e_s_i_a_n _s_u_r_v_i_v_a_l _r_e_g_r_e_s_s_i_o_n _w_i_t_h _a_n _e_r_r_o_r _d_i_s_t_r_i_b_u_t_i_o_n
_e_x_p_r_e_s_s_e_d _a_s _a~_n_o_r_m_a_l _m_i_x_t_u_r_e _w_i_t_h _u_n_k_n_o_w_n _n_u_m_b_e_r _o_f _c_o_m_p_o_n_e_n_t_s

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

     A function to sample from the posterior distribution for a
     survival regression  model

 log(T[i,l]) = beta'*x[i,l] + b[i]'*z[i,l] + epsilon[i,l], i=1,...,N, l=1,...,n[i],

     where distribution of epsilon[i,l] is specified as a normal
     mixture with unknown number of components as in Richardson and
     Green (1997) and random effect b[i] is normally distributed.

     See Kom&#225rek (2006) or Kom&#225rek and Lesaffre (2007) for more
     detailed description of prior assumptions.

     Sampled values are stored on a disk to be further worked out by
     e.g. 'coda' or 'boa'.

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

     bayessurvreg1(formula, random,
        data = parent.frame(), subset,
        na.action = na.fail,
        x = FALSE, y = FALSE, onlyX = FALSE,
        nsimul = list(niter = 10, nthin = 1, nburn = 0,
                      nnoadapt = 0, nwrite = 10),
        prior = list(kmax = 5, k.prior = "poisson", poisson.k = 3,
                     dirichlet.w = 1,
                     mean.mu = NULL, var.mu = NULL,
                     shape.invsig2 = 1.5,
                     shape.hyper.invsig2 = 0.8, rate.hyper.invsig2 = NULL,
                     pi.split = NULL, pi.birth = NULL,
                     Eb0.depend.mix = FALSE),
        prior.beta, prior.b, prop.revjump,
        init = list(iter = 0, mixture = NULL, beta = NULL,
                    b = NULL, D = NULL,
                    y = NULL, r = NULL, otherp = NULL, u = NULL),
        store = list(y = TRUE, r = TRUE, b = TRUE, u = TRUE,
                     MHb = FALSE, regresres = FALSE),
        dir = getwd(),
        toler.chol = 1e-10, toler.qr = 1e-10, ...)

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

 formula: model formula for the `fixed' part of the model, i.e. the
          part that specifies beta*x[i,l]. See 'survreg' for further
          details. Intercept is implicitely included in the model by
          estimation of the error distribution. As a consequence '-1'
          in the model formula does not have any effect on the model.

          The left-hand side of the 'formula' must be an~objecy created
          using 'Surv'.

          If 'random' is used then the formula must contain an
          identification of clusters in the form 'cluster(id)', where
          'id' is a name of the variable that determines clusters, e.g.

            'Surv(time, event)~gender + cluster(id)'.

  random: formula for the `random' part of the model, i.e. the part
          that specifies b[i]'*z[i,l]. If omitted, no random part is
          included in the model. E.g. to specify the model with a
          random intercept, say 'random=~1'. All effects mentioned in
          'random' should also be mentioned on the right-hand side of
          'formula'.

          When some random effects are included the random intercept is
          added by default. It can be removed using e.g. 'random=~-1 +
          gender'. 

    data: optional data frame in which to interpret the variables
          occuring in the formulas.

  subset: subset of the observations to be used in the fit.

na.action: function to be used to handle any 'NA's in the data. The
          user is discouraged to change a default value 'na.fail'.

       x: if 'TRUE' then the 'X' matrix is returned. This matrix
          contain all columns appearing in both 'formula' and 'random'
          parameters.

       y: if 'TRUE' then the 'y' matrix (of log-survival times) is
          returned.

   onlyX: if TRUE, no McMC is performed. The function returns only a
          design matrix of your model (intercept excluded). It might be
          useful to set up correctly a parameter for a block update of
          beta (regression parameters related to the fixed effects) and
          gamma (means of the random effects, random intercept
          excluded) parameters in the model if Metropolis-Hastings is
          to be used instead of default Gibbs.

  nsimul: a list giving the number of iterations of the McMC and other
          parameters of the simulation.

          _n_i_t_e_r total number of sampled values after discarding thinned
               ones, burn-up included.

          _n_t_h_i_n thinning interval.

          _n_b_u_r_n number of sampled values in a burn-up period after
               discarding thinned values. This value should be smaller
               than 'niter'. If not, 'nburn' is set to 'niter - 1'. It
               can be set to zero.

          _n_n_o_a_d_a_p_t applicable if some blocks of parameters are updated
               using an adaptive Metropolis algorithm. This is a number
               of sampled values that are generated using an initial
               and fixed proposal covariance matrix. It should be
               smaller or equal to 'nburn'. If not, 'nnoadapt' is set
               to 'nburn'.

          _n_w_r_i_t_e an interval at which sampled values are written to
               files. 

   prior: a list that identifies prior hyperparameters and prior
          choices. See accompanying paper for more details. Some prior
          parameters can be guessed by the function itself. If you want
          to do so, set such parameters to 'NULL'. Set to 'NULL' also
          the parameters that are not needed in your model.

          _k_m_a_x value of k[max], upper limit for the number of mixture
               components. Its high values like 100 will usually
               correspond to infinity.

          _k._p_r_i_o_r a string specifying the prior distribution of k,
               number of mixture components. Valid are either
               ``poisson'', ``uniform'', or ``fixed''. When ``fixed''
               is given then the number of mixture components is not
               sampled.

          _p_o_i_s_s_o_n._k prior hyperparameter lambda for the number of
               mixture components $k$ if Poisson prior for this
               parameter is used.

          _d_i_r_i_c_h_l_e_t._w prior hyperparameter delta for the Dirichlet
               distribution of mixture weights w[1],...w[k].

          _m_e_a_n._m_u prior hyperparameter xi for the mean of the normal
               prior for mixture means mu[1],...,mu[k].

          _v_a_r._m_u prior hyperparameter kappa for the variance of the
               normal prior for mixture means mu[1],...,mu[k].

          _s_h_a_p_e._i_n_v_s_i_g_2 prior hyperparameter zeta for the shape of the
               inverse-gamma distribution for the mixture variances
               sigma[1]^2,...,sigma[k]^2.

          _s_h_a_p_e._h_y_p_e_r._i_n_v_s_i_g_2 prior hyperparameter (shape) g for the
               gamma distribution of the parameter eta. Remember, eta
               is a scale parameter of the inverse-gamma distribution
               for the mixture variances sigma[1]^2,...,sigma[k]^2.

          _r_a_t_e._h_y_p_e_r._i_n_v_s_i_g_2 prior hyperparameter (rate) h for the
               gamma distribution of the parameter eta. Remember, eta
               is a scale parameter of the inverse-gamma distribution
               for the mixture variances sigma[1]^2,...,sigma[k]^2.

          _p_i._s_p_l_i_t probabilities of a split move within the reversible
               jump McMC. It must be a vector of length equal to 'kmax'
               with the first component equal to 1 and the last
               component equal to 0. If 'NULL' 2nd to (k-1)th
               components are set to 0.5.

          _p_i._b_i_r_t_h probabilities of a birth move within the reversible
               jump McMC. It must be a vector of length equal to 'kmax'
               with the first component equal to 1 and the last
               component equal to 0. If 'NULL' 2nd to (k-1)th
               components are set to 0.5.

          _E_b_0._d_e_p_e_n_d._m_i_x this will normally be 'FALSE'. Setting this
               option to 'TRUE' served for some experiments during the
               development of this function. In principle, when this is
               set to 'TRUE' and the random intercept is included in
               the model then it is assumed that the mean of the random
               intercept is not zero but sum[j=1][k] w[j]*mu[j], i.e.
               the mean of the random intercept depends on mixture.
               However, this did not werk too well.    

prior.beta: a list defining the blocks of beta parameters (both fixed
          effects and means of random effects, except the random
          intercept) that are to be updated together (in a block), a
          description of how they are updated and a specification of
          priors. The list is assumed to have the following components.

          _m_e_a_n._p_r_i_o_r a vector specifying a prior mean for each beta
               parameter in the model.

          _v_a_r._p_r_i_o_r a vector specifying a prior variance for each beta
               parameter. It is recommended to run the function
               'bayessurvreg1' first with its argument 'onlyX' set to
               'TRUE' to find out how the betas are sorted. They must
               correspond to a design matrix X.

          _b_l_o_c_k_s a list with the following components.

               _i_n_d._b_l_o_c_k a list with vectors with indeces of columns of
                    the design matrix X defining the effect of betas in
                    the block. If not specified, all beta parameters
                    corresponding to fixed effects are updated in one
                    block and remaining beta parameters (means of
                    random effects) in the second block using the Gibbs
                    move.

               _c_o_v._p_r_o_p a list with vectors with a lower triangle of
                    the covariance matrix which is used in the normal
                    proposal (use a command 'lower.tri' with 'diag =
                    TRUE' to get a lower triangle from a matrix) when
                    one of the Metopolis-like algorithms is used for a
                    given block. This matrix is used at each iteration
                    if the given block is updated using a standard
                    random-walk Metropolis-Hastings step. If the block
                    is updated using an adaptive Metropolis step this
                    matrix is used only at start. If not specified and
                    Metropolis-like algorith is required a diagonal
                    matrix with prior variances for corresponding beta
                    on a diagonal is used. It is set to a vector of
                    zeros of appropriate length when the Gibbs move is
                    required for a given block.


          _t_y_p_e._u_p_d a character vector specifying the type of the update
               that will be used for each block. Valid are substrings
               of either "gibbs" or "adaptive.metropolis" or
               "random.walk.metropolis". Default is "gibbs" for all
               blocks.

          _m_e_a_n._s_a_m_p_l_e_d a vector of means of up to now sampled values.
               This component is useful when the adaptive Metropolis
               algorithm is used and we do not start from the beginning
               (e.g. already several iterations of McMC have already
               been performed). Otherwise, this component does not have
               to be filled.

          _e_p_s._A_M a vector with epsilon from the adaptive Metropolis
               algorithm for each block.

          _s_d._A_M a vector specifying s[d], d = 1, ..., D numbers from
               the adaptive Metropolis algorithm for each dimension.
               This vector must be of length equal at least to the
               length of the longest block. Defaults values are
               (1/d)*2.4^2 where d denotes a length of the block.

          _w_e_i_g_h_t._u_n_i_f a vector specifying the weight of the uniform
               component in the proposal for each block. If not
               specified, it is equal to 0.5 for all parameters.

          _h_a_l_f._r_a_n_g_e._u_n_i_f a vector of same length as the number of
               columns in the design matrix X specifying the half range
               of the uniform component of the proposal.     

 prior.b: a list defining the way in which the random effects are to be
          updated and the specification of priors for random effects
          related parameters. The list is assumed to have following
          components.

          _p_r_i_o_r._D a string defining the prior distribution for the
               covariance matrix of random effects D. It can be either
               ``inv.wishart'' or ``sduniform''.

               _i_n_v._w_i_s_h_a_r_t in that case is assumed that the prior
                    distribution of the matrix D is Inverse-Wishart
                    with degrees of freedom equal to tau and a scale
                    matrix equal to S. When D is a matrix q x q a prior
                    expectation of D is equal to (1/(tau - q - 1))S if
                    tau > q + 1. For q - 1 < tau <= q + 1 a prior
                    expectation is not finite.         Degrees of
                    freedom parameter tau does not have to be an
                    integer. It has to only satisfy a condition tau > q
                    - 1. 'prior.b$df.D' gives a prior degrees of
                    freedom parameter tau and 'prior.b$scale.D'
                    determines the scale matrix D. This is also the
                    default choice.

               _s_d_u_n_i_f_o_r_m this can be used only when the random effect
                    is univariate. Then the matrix D is just a scalar
                    and the prior of sqrt(D) (standard deviation of the
                    univariate random effect) is assumed to be uniform
                    on interval (0, S). The upper limit S is given by
                    'prior.b$scale.D'. 


          _d_f._D degrees of freedom parameter tau in the case that the
               prior of the matrix D is inverse-Wishart.

          _s_c_a_l_e._D a lower triangle of the scale matrix S in the case
               that the prior of the matrix D is inverse-Wishart or the
               upper limit S of the uniform distribution in the case
               that sqrt(D) ~ Unif(0, S).

          _t_y_p_e._u_p_d a character vector specifying the type of the
               update. Valid are substrings of either
               "random.walk.metropolis" or "gibbs". Default is "gibbs".
               In contrast to beta parameters, all random effects are
               updated using the same type of the move. If
               "random.walk.metropolis" is used, random effects may be
               divided into blocks in which they are updated. With
               "gibbs", there is only one block defined for all random
               effects. which are updated in one step using its full
               conditional distribution.

          _b_l_o_c_k_s a list with the following components. This is set to
               NULL if 'type.upd = "gibbs"'.      

               _i_n_d._b_l_o_c_k a list with vectors with indeces of random
                    effects defining the block. Random intercept has
                    always an index 1, remaining random effects have
                    subsequent indeces according to their appearance in
                    the design matrix X.

               _c_o_v._p_r_o_p a list with vectors with a lower triangle of
                    the covariance matrix which is used in the normal
                    proposal (use a command 'lower.tri' with 'diag =
                    TRUE' to get a lower triangle from a matrix) for a
                    given block when

                      'type.upd = "random.walk.metropolis"'.



          _w_e_i_g_h_t._u_n_i_f a vector specifying the weight of the uniform
               component in the proposal for each block when

                 'type.upd = "random.walk.metropolis"'.

               If not specified, it is equal to 0.5 for all parameters.
               It is set to NULL if 'type.upd = "gibbs"'. 

          _h_a_l_f._r_a_n_g_e._u_n_i_f a vector of same length as the number of
               random effects specifying the half range of the uniform
               component of the proposal when 'type.upd =
               "random.walk.metropolis"'. It is set to NULL if
               'type.upd = "gibbs"'.       

prop.revjump: a list of values defining in which way the reversible
          jumps will be performed. 

          _a_l_g_o_r_i_t_h_m a string defining the algorithm used to generate
               canonical proposal vectors u = (u[3k+1], ..., u[3kmax])
               where u[3k+1], u[3k+2], u[3k+3] are directly used when a
               jump to a space of higher dimension is proposed. These
               canonical proposal vectors are further transformed to
               give desired parameters (mixture component's weight,
               mean and variance).  Valid values of
               'prop.revjump$algorithm' are substrings of "basic",
               "independent.av", "correlated.av". '"basic"' means that
               both components of vectors u and vectors u in time are
               generated independently from a standard uniform
               distribution. This corresponds to a basic reversible
               jumps McMC algorithm of Green (1995). Other two methods
               implement an auxiliary variable method of Brooks et al.
               (2003). The first one an independent auxiliary variable
               method where vectors u may be correlated in time however
               their components are independent and the second one the
               correlated auxiliary method where vectors u are
               correlated in time and also their components may be
               correlated. In both cases components of vectors u follow
               marginally a standard uniform distribution. A moody ring
               method of Brooks et al. (2003) is used to generate u
               vectors.

          _m_o_o_d_y._r_i_n_g parameters for the moody ring when 'algorithm' is
               either "independent.av" or "correlated.av". This is a
               two component vector with both components taking values
               between 0 and 0.5 defining the strength of a correlation
               in time and between the components of u vectors. This
               vector is ignored when 'algorithm = "basic"'. The first
               component of this vector determines dependence between u
               vectors in time (epsilon in Brooks et al. (2003)), the
               second component determines dependence between
               components of u vectors (delta in Brooks et al. (2003)).
               The second compoenent is ignored when 'algorithm =
               "independent.av"'. Note that both epsilon and delta do
               not have a meaning of correlation. They determine a
               range of additional uniform distributions. So that their
               values equal to 0 mean perfect correlation and their
               values equal to 0.5 mean independence. I.e.
               "correlated.av" with delta = 0.5 is same as
               "independent.av" and "correlated.av" with delta = 0.5,
               epsilon = 0.5 is same as "basic".

          _t_r_a_n_s_f_o_r_m._s_p_l_i_t._c_o_m_b_i_n_e a description of how the canonical
               variables u are to be transformed to give new values of
               mixture component's weight, mean and variance when a
               split move is proposed. Possible values are substrings
               of "richardson.green", "brooks" and "identity". In all
               cases, the (0, 1) canonical variables u are transformed 
               to (0, 1) variates v that are than used to compute new
               values of mixture component's weight, mean and variance
               using a method of moments matching described in
               Richardson and Green (1997). When "identity", no further
               transformation is performed, when "richardson.green", u
               vectors are transformed such that the components of
               resulting v vectors follow independently beta
               distributions with parameters given further by 'p =
               prop.revjump$transform.split.combine.parms' such that in
               the triplet of v's used in a particular split move, v[1]
               ~ beta(p[1], p[2]), v[2] ~ beta(p[3], p[4]), v[3] ~
               beta(p[5], p[6]). When "brooks" v[2] is further
               transformed by |2*v[2] - 1|. Default values of

                 'prop.revjump$transform.split.combine$parms'

               is 'c(2, 2, 2, 2, 1, 1)'.

          _t_r_a_n_s_f_o_r_m._s_p_l_i_t._c_o_m_b_i_n_e._p_a_r_m_s see above.

          _t_r_a_n_s_f_o_r_m._b_i_r_t_h._d_e_a_t_h a description of how the canonical
               variables u are to be transformed to give new values of
               mixture component's weight, mean and variance when a
               birth move is proposed. At this moment only one value is
               possible: "richardson.green" implementing the proposal
               as in Richardson and Green (1997).

    init: a list of the initial values to start the McMC. Set to 'NULL'
          such parameters that you want the program should itself
          sample for you or parameters that are not needed in your
          model.

          _i_t_e_r index of the iteration to which initial values
               correspond, usually zero.

          _m_i_x_t_u_r_e initial mixture for the error random variable
               epsilon. It must a vector of length '1 + 3*kmax', where
               'mixture[1]' gives initial number of mixture of
               components k, 'mixture[2:(k+1)]' gives initial mixture
               weights, 'mixture[(2+kmax):(2+kmax+k-1)]' gives initial
               mixture means,  'mixture[(2+2*kmax):(2+2*kmax+k-1)]'
               gives initial mixture variances. Remaining components of
               this vector are ignored.

          _b_e_t_a initial values of regression parameters in the same
               order as columns of the design matrix 'X'. Call the
               function 'bayessurvreg1' with 'onlyX = TRUE' to see how
               the columns are sorted. Remember, 'beta' in this
               function contains both fixed effects beta and means of
               random effect gamma in the notation of the accompanying
               paper except the mean of the random intercept which is
               always zero.

          _b initial values of random effects b[i] for each cluster.
               This must a matrix of size q x N or a vector of length
               q*N, where q is a number of random effects and N number
               of clusters, one column per cluster.

          _D initial value for the covariance matrix of random effects
               D. Only its lower triangle must be given in a vector,
               e.g. 'c(d[1,1], d[2,1], d[3,1], d[2,2], d[3,2], d[3,3])'
               for a matrix 3 x 3.

          _y initial values of true log-event times. This must be a
               vector of length sum[i=1][N] n[i].

          _r initial values of component labels r_{i,l}. This must be a
               vector of length sum[i=1][N] n[i].

          _o_t_h_e_r_p initial values for other parameters. At this moment,
               only a value of the parameter eta is given here.

          _u initial canonical proposal vector of length 3*kmax. When
               initial number of compoents given by 'init$mixture[1]'
               is k, effectively only last 3*kmax - 3*k components of
               the initial u vector are used. Further, when
               'prop.revjump$algorithm = "correlated.av"', the first
               component of 'init$u' ('init$u[1]') contains an initial
               mood parameter (c[0] in Brooks et al. (2003)) for the
               moody ring.

   store: a list that defines which sampled values besides regression
          parameters beta, means of random effects gamma (both stored
          in a file called 'beta.sim'), a covariance matrix of random
          effects D (stored in a file 'D.sim'), the mixture (stored in
          file 'mixmoment.sim, mweight.sim, mmean.sim, mvariance.sim'),
          values of other parameters - eta (stored in a file
          'otherp.sim'), values of log-likelihoods (stored in a file
          'loglik.sim'), information concerning the performance of the
          reversible jump McMC and acceptance of regression parameters
          (stored in a file 'MHinfo.sim'), iteration indeces (stored in
          a file 'iteration.sim') are to be stored. The list 'store'
          has the following components.

          _y if 'TRUE' sampled true log-event times are  stored.

          _r if 'TRUE' sampled component labels are stored.

          _b if 'TRUE' sampled values of random effects b[i] are stored.

          _u if 'TRUE' sampled values of canonical proposal vectors for
               the reversible jump McMC are stored.

          _M_H_b if 'TRUE' information concerning the performance of the
               Metropolis-Hastings algorithm for the update of random
               effects (if used instead of a dafault Gibbs) is stored.

          _r_e_g_r_e_s_r_e_s if 'TRUE' sampled values of regression residuals at
               each iteration are stored. The regression residual is
               defined as res[i,l] = log(t[i,l]) - beta'*x[i,l] -
               b[i]'*z[i,l].

          In the case that either 'store$y', or 'store$r', or
          'store$b', or 'store$u' are 'FALSE', only the last values of
          either 'y', or 'r', or 'b', or 'u' at the time of writting of
          remaining quantities are stored in appropriate files (without
          headers) to be possibly used by 'bayessurvreg1.files2init'
          function.   

     dir: a string that specifies a directory where all sampled values
          are to be stored.

toler.chol: tolerance for the Cholesky decomposition.

toler.qr: tolerance for the QR decomposition.

     ...: who knows?

_V_a_l_u_e:

     A list of class 'bayessurvreg' containing an information
     concerning the initial values and prior choices.

_F_i_l_e_s _c_r_e_a_t_e_d:

     Additionally, the following files with sampled values are stored
     in a directory specified by 'dir' parameter of this function (some
     of them are created only on request, see 'store' parameter of this
     function).

     _i_t_e_r_a_t_i_o_n._s_i_m one column labeled 'iteration' with indeces of McMC
          iterations to which the stored sampled values correspond.

     _l_o_g_l_i_k._s_i_m two columns labeled 'loglik' and 'randomloglik'.

 'loglik' = sum[i=1][N]sum[l=1][n[i]] (log(1/sqrt(2*pi*sigma[r[i,l]]^2)) - 0.5*sigma[r[i,l]]^(-2)*(y[i,l] - beta'*x[i,l] - b[i]*z[i,l]-mu[r[i,l]])^2),

          where y[i,l] denotes (sampled) _(i,l)_th true log-event time,
          b[i] sampled value of the random effect vector for the _i_th
          cluster, beta sampled value of the regression parameter beta
          and k, w[j], mu[j], sigma[j]^2, j = 1,..., k sampled mixture
          at each iteration.

              'randomloglik' = sum[i=1][N] log(g(b[i])),

          where g denotes a density of (multivariate) normal
          distribution N(gamma, D), where gamma is a sampled value of
          the mean of random effect vector and D is a sampled value of
          the covariance matrix of the random effects at each
          iteration.      

     _m_i_x_m_o_m_e_n_t._s_i_m three columns labeled 'k', 'Intercept' and 'Scale'.
          These are the number of mixture components, mean and standard
          deviation of the sampled error distribution (mixture) at each
          iteration.

     _m_w_e_i_g_h_t._s_i_m each row contains mixture weights w[1],...,w[k] at
          each iteration. From the header of this file, maximal number
          of mixture components specified in the prior can be derived.

     _m_m_e_a_n._s_i_m each row contains mixture means mu[1],...,mu[k] at each
          iteration. From the header of this file, maximal number of
          mixture components specified in the prior can be derived.

     _m_v_a_r_i_a_n_c_e._s_i_m each row contains mixture variances
          sigma2[1],...,sigma2[k] at each iteration. From the header of
          this file, maximal number of mixture components specified in
          the prior can be derived.    

     _b_e_t_a._s_i_m columns labeled according to name of the design matrix.
          These are sampled values of regression parameters beta and
          means of random effects gamma (except the mean of the random
          intercept which is zero).

     _b._s_i_m columns labeled 'nameb[1].id[1], ..., nameb[q].id[1], ...,
          nameb[1].id[N], ..., nameb[q].id[N]', where 'q' is a
          dimension of the random effect vector b[i] and 'N'{N} number
          of clusters. 'nameb' is replaced by appropriate column name
          from the design matrix and 'id' is replaced by identificator
          of the clusters. This gives sampled values of the random
          effects for each cluster.

     _D._s_i_m columns labeled 'det, D.s.t, s = 1,..., q, t = s,...,q',
          where 'q' is dimension of the random effect vector b[i].
          Column 'det' gives a determinant of the covariance matrix D
          of the random effects at each iteration, remaining columns
          give a lower triangle of this matrix at each iteration.

     _Y._s_i_m columns labeled 'Y[m]' where 'm' goes from 1 to
          sum[i=1][N]n_i. This gives sampled log-event times for each
          observation in the dataset at each iteration.

     _r._s_i_m columns labeled 'r[m]' where 'm' goes from 1 to
          sum[i=1][N]n_i. This gives sampled mixture labels for each
          observation in the dataset at each iteration.

     _o_t_h_e_r_p._s_i_m Currently only one column labeled 'eta' that gives
          sampled values of the hyperparameter eta.

     _M_H_i_n_f_o._s_i_m this gives the information concerning the performance
          of reversible jump algorithm and a sampler of regression
          parameters beta and means of random effects gamma. It has
          columns

          '_a_c_c_e_p_t._s_p_l._c_o_m_b' relative frequency of accepted
               split-combine moves up to that iteration.

          '_s_p_l_i_t' relative frequency of proposed split moves up to that
               iteration.

          '_a_c_c_e_p_t._b_i_r_t_h._d_e_a_t_h' relative frequency of accepted
               birth-death moves up to that iteration.

          '_b_i_r_t_h' relative frequency of proposed birth moves up to that
               iteration.

          '_b_e_t_a._b_l_o_c_k._m' with 'm' going from 1 to number of defined
               blocks of beta parameters. This gives a relative
               frequency of accepted proposals for each block up to
               that iteration. When Gibbs move is used, these should be
               columns of ones.


     _M_H_b_i_n_f_o._s_i_m this gives the information concerning the performance
          of a sampler for random effects (relative frequency of
          accepted values for each cluster and each block of random
          effects updated together). When Gibbs move is used only ones
          are seen in this file.

     _u._s_i_m Sampled values of canonical proposal variables for
          reversible jump algorithm are stored here. This file is
          useful only when trying to restart the simulation from some
          specific point.

     _r_e_g_r_e_s_r_e_s._s_i_m columns labeled 'res[m]' where 'm' goes from 1 to
          sum[i=1][N]n_i. This stores so called regression residuals
          for each observation at each iteration. This residual is
          defined as

 res[i,l] = y[i,l] - beta'*x[i,l] - b[i]'*z[i,l], i=1,...,N, l=1,...,n[i],

          where y[i,l] is a (sampled) log-event time at each iteration.

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

     Arno&#353t Kom&#225rek komarek@karlin.mff.cuni.cz

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

     Kom&#225rek, A. (2006). _Accelerated Failure Time Models for
     Multivariate Interval-Censored Data with Flexible Distributional
     Assumptions_. PhD. Thesis, Katholieke Universiteit Leuven,
     Faculteit Wetenschappen.

     Kom&#225rek, A. and Lesaffre, E. (2007). Bayesian accelerated
     failure time model for correlated interval-censored data with a
     normal mixture as an error distribution. _Statistica Sinica_,
     *17*, 549-569.

     Brooks, S. P., Giudici, P., and Roberts, G. O. (2003). Efficient
     construction of reversible jump Markov chain Monte Carlo proposal
     distribution (with Discussion). _Journal of the Royal Statistical
     Society B,_ *65,* 3 - 55.

     Green, P. J. (1995). Reversible jump MCMC computation and Bayesian
     model determination. _Biometrika,_ *82,* 711-732.

     Richardson, S., and Green, P. J. (1997). On Bayesian analysis of
     mixtures with unknown number of components (with Discussion).
     _Journal of the Royal Statistical Society B,_ *59,* 731 - 792.

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

     ## See the description of R commands for
     ## the models described in
     ## Komarek (2006),
     ## Komarek and Lesaffre (2007).
     ## 
     ## R commands available
     ## in the documentation
     ## directory of this package as
     ## cgd.pdf, cgd.R
     ## tandmobMixture.pdf, tandmobMixture.R

