# remlscoregamma

##### Approximate REML for gamma regression with structured dispersion

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

##### Value

- List with the following components:
beta Vector of regression coefficients for predicting the mean se.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

##### item

details

##### eqn

$\mu_i=E(y_i)$

##### 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 $

*Documentation reproduced from package statmod, version 0.6, License: GPL version 2 or newer*