remlscoregamma            package:statmod            R Documentation

_A_p_p_r_o_x_i_m_a_t_e _R_E_M_L _f_o_r _g_a_m_m_a _r_e_g_r_e_s_s_i_o_n _w_i_t_h _s_t_r_u_c_t_u_r_e_d _d_i_s_p_e_r_s_i_o_n

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

     Estimates structured dispersion effects using approximate REML
     with gamma responses.

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

     remlscoregamma(y,X,Z,mlink="log",dlink="log",trace=FALSE,tol=1e-5,maxit=40)

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

       y: numeric vector of responses

       X: design matrix for predicting the mean

       Z: design matrix for predicting the variance

   mlink: character string or numeric value specifying link for mean
          model

   dlink: character string or numeric value specifying link for
          dispersion model

   trace: Logical variable. If true then output diagnostic information
          at each iteration.

     tol: Convergence tolerance

   maxit: Maximum number of iterations allowed

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

     Write mu_i=E(y_i) for the expectation of the ith response and
     s_i=var(y_i). We assume the heteroscedastic regression model

                          mu_i=*x*_i^T*beta*


                    log(sigma^2_i)=*z*_i^T*gamma*,

     where *x*_i and *z*_i are vectors of covariates, and *beta* and
     *gamma* are vectors of regression coefficients affecting the mean
     and variance respectively.

     Parameters are estimated by maximizing the REML likelihood using
     REML scoring as described in Smyth and Verbyla (2001). See also
     Smyth and Verbyla (1999a,b).

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

     List with the following components: 

    beta: Vector of regression coefficients for predicting the mean

 se.beta: <Standard errors for beta

   gamma: Vector of regression coefficients for predicting the variance

  se.gam: Standard errors for gamma

      mu: Estimated means

     phi: Estimated dispersions

deviance: Minus twice the REML log-likelihood

       h: Leverages

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

     Smyth, G. K., and Verbyla, A. P. (1999a). Adjusted likelihood
     methods for modelling dispersion in generalized linear models.
     _Environmetrics_ 10, 695-709.  <URL:
     http://www.statsci.org/smyth/pubs/earlier.html>

     Smyth, G. K., and Verbyla, A. P. (1999b). Double generalized
     linear models: approximate REML and diagnostics. In _Statistical
     Modelling: Proceedings of the 14th International Workshop on
     Statistical Modelling_, Graz, Austria, July 19-23, 1999, H.
     Friedl, A. Berghold, G. Kauermann (eds.), Technical University,
     Graz, Austria, pages 66-80. <URL:
     http://www.statsci.org/smyth/pubs/earlier.html>

     Smyth, G. K., and Verbyla, A. P. (2001). Leverage adjustments for
     dispersion modelling in generalized nonlinear models. Unpublished
     technical report. <URL: http://www.statsci.org/smyth/pubs/dglm.ps>

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

     data(welding)
     attach(welding)
     y <- Strength
     X <- cbind(1,(Drying+1)/2,(Material+1)/2)
     colnames(X) <- c("1","B","C")
     Z <- cbind(1,(Material+1)/2,(Method+1)/2,(Preheating+1)/2)
     colnames(Z) <- c("1","C","H","I")
     out <- remlscoregamma(y,X,Z)

