|dglm||Double generalized linear models|
|formula||a formula expression as for glm, of the form response ~ predictors. See the documentation of lm and formula for details. As for glm, this specifies the linear predictor for modelling the mean. A term of the form offset(expression) is allowed.|
|dformula||a formula expression of the form ~ predictor, the response being ignored. This specifies the linear predictor for modelling the dispersion. A term of the form offset(expression) is allowed.|
|dlink||link function for modelling the dispersion. Any link function accepted by the quasi family is allowed, including power(x). See details below.|
|method||the method used to estimate the dispersion parameters; the default is "reml" for restricted maximum likelihood and the alternative is "ml" for maximum likelihood. Upper case and partial matches are allowed.|
|mustart||numeric vector giving starting values for the fitted values or expected responses. Must be of the same length as the response, or of length 1 if a constant starting vector is desired. Ignored if betastart is supplied.|
|betastart||numeric vector giving starting values for the regression coefficients in the link-linear model for the mean.|
|phistart||numeric vector giving starting values for the dispersion parameters.|
|control||a list of iteration and algorithmic constants. See dglm.control for their names and default values. These can also be set as arguments to dglm itself.|
|ykeep||logical flag: if TRUE, the vector of responses is returned.|
|xkeep||logical flag: if TRUE, the model.matrix for the mean model is returned.|
|zkeep||logical flag: if TRUE, the model.matrix for the dispersion model is returned.|
g(mi) = xiTb, h(si) = ziTa,
where xi and zi are vectors of covariates, and b and a are vectors of regression cofficients affecting the mean and dispersion respectively. The argument dlink specifies h. See family in the S-Plus help for how to specify g. The optional arguments mustart, betastart and phistart specify starting values for mi, b and si respectively.
The parameters b are estimated as for an ordinary glm. The parameters a are estimated by way of a dual glm in which the deviance components of the ordinary glm appear as responses. The estimation procedure alternates between one iteration for the mean submodel and one iteration for the dispersion submodel until overall convergence.
The output from dglm, out say, consists of two glm objects (that for the dispersion submodel is out$dispersion.fit) with a few more components for the outer iteration and overall likelihood. The summary and anova functions have special methods for dglm objects. Any generic function which has methods for glms or lms will work on out, giving information about the mean submodel. Information about the dispersion submodel can be obtained by using out$dispersion.fit as argument rather than out itself. In particular drop1(out,scale=1) gives correct score statistics for removing terms from the mean submodel, while drop1(out$dispersion.fit,scale=2) gives correct score statistics for removing terms from the dispersion submodel.
Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004