# remlscoregamma

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##### 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
character string or numeric value specifying link for mean model
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 $\mu_i=E(y_i)$ for the expectation of the $i$th response and $s_i=(y_i)$. We assume the heteroscedastic regression model $$\mu_i=\bold{x}_i^T\bold{\beta}$$ $$\log(\sigma^2_i)=\bold{z}_i^T\bold{\gamma},$$ 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 and Verbyla (2001). See also Smyth and Verbyla (1999a,b). Smyth, G. K., and Verbyla, A. P. (1999a). Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics 10, 695-709. http://www.statsci.org/smyth/pubs/earlier.html Smyth, G. K., and Verbyla, A. P. (1999b). Double generalized linear models: approximate REML and diagnostics. In Statistical Modelling: Proceedings of the 14th International Workshop on Statistical Modelling, Graz, Austria, July 19-23, 1999, H. Friedl, A. Berghold, G. Kauermann (eds.), Technical University, Graz, Austria, pages 66-80. http://www.statsci.org/smyth/pubs/earlier.html Smyth, G. K., and Verbyla, A. P. (2001). Leverage adjustments for dispersion modelling in generalized nonlinear models. Unpublished technical report. http://www.statsci.org/smyth/pubs/dglm.ps 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

##### Value

• List with the following components:
• betaVector of regression coefficients for predicting the mean
• se.beta
• gammaVector of regression coefficients for predicting the variance
• se.gamStandard errors for gamma
• muEstimated means
• phiEstimated dispersions
• devianceMinus twice the REML log-likelihood
• hLeverages

##### Aliases
• remlscoregamma
Documentation reproduced from package statmod, version 1.3.6, License: LGPL (>= 2)

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