logpoissonRE             package:glmmAK             R Documentation

_P_o_i_s_s_o_n _l_o_g-_l_i_n_e_a_r _r_e_g_r_e_s_s_i_o_n
_w_i_t_h _r_a_n_d_o_m _e_f_f_e_c_t_s

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

     This function implements MCMC sampling for the Poisson log-linear
     model. Details are given in Kom&#225rek and Lesaffre (2007). On as
     many places as possible, the same notation as in this paper is
     used also in this manual page.

     In general, the following log-linear model for response Y is
     assumed:

                            log(Y) = eta,

     where the form of the linear predictor eta depends on whether a
     hierarchical centering is used or not. In the following, beta
     denotes fixed effects and b random effects.

     *No hierarchical centering (DEFAULT)*
      The linear predictor has the following form

                   eta= beta'(x', x(b)') + b'x(b),

     where b is a vector of random effects with zero location. 

     *Hierarchical centering*
      The linear predictor has the following form

                        eta= beta'x + b'x(b),

     b is a vector of random effects with location alpha.

     For description of the rest of the model, see 'cumlogitRE'.

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

     logpoissonRE(y, x, xb, offset=0, cluster,                       
           intcpt.random=FALSE,
           hierar.center=FALSE,                       
           drandom=c("normal", "gspline"),
           prior.fixed,
           prior.random,
           prior.gspline,
           init.fixed,
           init.random,
           init.gspline,                 
           nsimul = list(niter=10, nthin=1, nburn=0, nwrite=10),
           store = list(ecount=FALSE, b=FALSE, alloc=FALSE, acoef=FALSE),
           dir=getwd(),
           precision=8)

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

       y: response vector taking integer values or zero. 

       x: vector, matrix or data.frame with covariates for *fixed*
          effects. 

      xb: vector, matrix or data.frame with covariates for *random*
          effects.

          If you want to include *random intercept*, do it by setting
          the argument 'intcpt.random' to 'TRUE'. The intercept column
          should not be included in 'xb'.     

  offset: optional vector of the offset term. 

 cluster: see 'cumlogitRE'.

intcpt.random: see 'cumlogitRE'.

hierar.center: see 'cumlogitRE'.

 drandom: see 'cumlogitRE'.

prior.fixed: see 'cumlogitRE'.

prior.random: see 'cumlogitRE'.

prior.gspline: see 'cumlogitRE'.

init.fixed: see 'cumlogitRE'.

init.random: see 'cumlogitRE'.

init.gspline: see 'cumlogitRE'.

  nsimul: see 'cumlogitRE'.

   store: list indicating which chains (out of these not stored by
          default) should be compulsory stored. The list has the
          logical components with the following names.

          _e_c_o_u_n_t if 'TRUE' values of individual predictive (expected)
               counts are stored.

          _b if 'TRUE' values of cluster specific random effects are
               stored.

          _a_l_l_o_c if 'TRUE' values of allocation indicators are stored.

          _a_c_o_e_f if 'TRUE' and distribution of random effects is given
               as a *bivariate* G-spline values of log-G-spline weights
               (a coefficients) are stored for all components.


     dir: see 'cumlogitRE'.

precision: see 'cumlogitRE'.

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

     See 'cumlogitRE.'

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


     _i_t_e_r_a_t_i_o_n._s_i_m see 'cumlogitRE'.

     _b_e_t_a_F._s_i_m sampled values of the fixed effects beta.

          *Note* that in models with *G-spline* distributed random
          effects which are not hierarchically centered, the average
          effect of the covariates involved in the random effects
          (needed for inference) is obtained as a sum of the
          corresponding beta coefficient and a scaled mean of the
          G-spline. beta coefficients adjusted in this way are stored
          in the file 'betaRadj.sim' (see below).

     _b_e_t_a_R._s_i_m sampled values of the location parameters alpha of the
          random effects when the *hierarchical centering* was used.

          *Note* that in models with *G-spline* distributed random
          effects which are hierarchically centered, the average effect
          of the covariates involved in the random effects (needed for
          inference) is obtained as a sum of the corresponding alpha
          coefficient and a mean of the G-spline.  alpha coefficients
          adjusted in this way are stored in the file 'betaRadj.sim'
          (see below).      

     _v_a_r_R._s_i_m see 'cumlogitRE'.

     _l_o_g_l_i_k._s_i_m see 'cumlogitRE'.

     _e_x_p_e_c_t_c_o_u_n_t._s_i_m sampled values of predictive (expected) counts for
          each observations.

          Created only if 'store$ecount' is 'TRUE'. 

     _b._s_i_m see 'cumlogitRE'.

_F_i_l_e_s _c_r_e_a_t_e_d _f_o_r _m_o_d_e_l_s _w_i_t_h _G-_s_p_l_i_n_e _d_i_s_t_r_i_b_u_t_e_d
  _r_a_n_d_o_m _e_f_f_e_c_t_s:

     See 'cumlogitRE'.

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

     Arno&#353t Kom&#225rek arnost.komarek[AT]mff.cuni.cz

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

     Agresti, A. (2002). _Categorical Data Analysis. Second edition_.
     Hoboken: John Wiley & Sons.

     Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1995). Efficient
     parametrisations for normal linear mixed models. _Biometrika_,
     *82*, 479-488.

     Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for
     Gibbs sampling. _Applied Statistics,_ *41*, 337-348.

     Neal, R. M. (2003). Slice sampling (with Discussion). _The Annals
     of Statistics,_ *31*, 705-767.

     Kom&#225rek, A. and Lesaffre, E. (2008). Generalized linear mixed
     model with a penalized Gaussian mixture as a random-effects
     distribution. _Computational Statistics and Data Analysis_, *52*,
     3441-3458.

     Molenberghs, G. and Verbeke, G. (2005). _Models for Discrete
     Longitudinal Data_. New York: Springer Science+Business Media.

_S_e_e _A_l_s_o:

     'logpoisson', 'cumlogitRE', 'poisson', 'glm'.

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

     ### See ex-Epileptic.pdf and ex-Epileptic.R
     ### available in the documentation
     ### to the package

