remlscore              package:statmod              R Documentation

_R_E_M_L _f_o_r _H_e_t_e_r_o_s_c_e_d_a_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:

     Fits a heteroscedastic regression model using residual maximum
     likelihood (REML).

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

     remlscore(y, X, Z, 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

   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 (2002).

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

     List with the following components: 

    beta: vector of regression coefficients for predicting the mean

 se.beta: vector of standard errors for beta

   gamma: vector of regression coefficients for predicting the variance

  se.gam: vector of standard errors for gamma

      mu: estimated means

     phi: estimated variances

deviance: minus twice the REML log-likelihood

       h: numeric vector of leverages

cov.beta: estimated covariance matrix for beta

 cov.gam: estimated covarate matrix for gamma

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

     Gordon Smyth

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

     Smyth, G. K. (2002). An efficient algorithm for REML in
     heteroscedastic regression. _Journal of Computational and
     Graphical Statistics_ *11*, 836-847.

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

     data(welding)
     attach(welding)
     y <- Strength
     # Reproduce results from Table 1 of Smyth (2002)
     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 <- remlscore(y,X,Z)
     cbind(Estimate=out$gamma,SE=out$se.gam)

