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., and Verbyla, A. P. (2002). Leverage adjustments for dispersion modelling in generalized nonlinear models.
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)
regression