remlscoregamma {statmod}R Documentation

Approximate REML for gamma regression with structured dispersion

Description

Estimates structured dispersion effects using approximate REML with gamma responses.

Usage

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

Arguments

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

Details

Write μ_i=E(y_i) for the expectation of the $i$th response and $s_i=var(y_i)$. We assume the heteroscedastic regression model

μ_i=x_i^Tβ

log(σ^2_i)=z_i^Tgamma,

where $x_i$ and $z_i$ are vectors of covariates, and $β$ 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).

Value

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

References

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

Examples

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)

[Package statmod version 1.2.4 Index]