item
detailseqn
$\mu_i=E(y_i)$var
(y_i)$.
We assume the heteroscedastic regression model
$$\mm_i=\bold{x}_i^T\bold{\beta}$$
$$\log(\sigma^2_i=\bold{z}_i^T\bold{\gamma},$$
where $x_i$ and $z_i$ are vectors of covariates, and $$ and $$ 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).
Smyth, G. K. (2002). An efficient algorithm for REML in heteroscedastic regression. Journal of Computational and Graphical Statistics 11, 1-12.
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)
regression