DHGLMMODELING: Defining the Fixed and Random Models for the Mean and Dispersion parameters in DHGLMs

Description

The DHGLMMODELING specifies a GLM, HGLM, DHGLM model for the mean parameters (mu), and a GLM, HGLM model for the overdispersion parameters (phi). GLM for mu, and GLM for phi are specified by adding only fixed terms to the linear predictors for the mu and phi, respectively. These are extended to HGLM for mu and HGLM for phi by adding some random terms. The DHGLM for mu is specified by allowing random effects for the variance of random effects in HGLM for mu. The LMatrix argument allows correlation structures to be defined for random terms. This is done by setting LMatrix to a matrix L that is used as a post-multiplier for the Z matrix of the corresponding random term.

Usage

DHGLMMODELING(Model="mean",Link=NULL,LinPred="constant",RandDist=NULL,
Offset=NULL,LMatrix=NULL,LinkRandVariance=NULL,LinPredRandVariance=NULL,
RandDistRandVariance="gaussian",
LinkRandVariance2=NULL,LinPredRandVariance2=NULL)

Arguments

Model

This option specifies a GLM, HGLM or DHGLM model for mu when Model="mean" (default), and a GLM or HGLM for phi when Model="dispersion".

Link

The link function for the linear predictor is specified by the option Link. For Model="mean", Link can be "identity", "logit", "probit", "cloglog", "log", or "inverse". For Model="dispersion", the choice is either "log" or "inverse". The default, sp

LinPred

The option LinPred specifies the fixed and random terms for the linear predictor for mu when specified as Model="mean" or for phi when Model="dispersion". For Model="mean", LinPred=y~x1+x2+(1|id1)+(1|id2) specifies y as the main response, x1 and x2 as

RandDist

The option RandDist specifies the distributions of the random terms represented in the option LinPred. It is set as a vector of distribution names from "gaussain" (default), "beta", "gamma", or "inverse-gamma" when Model="mean". For Model="dispersion"

Offset

The option Offset can be used to specify a known component to be included in the linear predictor specified by LinPred during fitting. This should be the default (NULL) or a numeric vector of length equal to that of the appropriate data.

LMatrix

The option LMatrix sets a matrix that is used as a post-multiplier for the model matrix of the corresponding random effects. This option allows correlation structures to be defined for random effects. For example, when specified as Model="mean" and Lma

LinkRandVariance

The option LinkRandVariance specifies the link function for the linear predictor of the random-effect variances. The choice is either "log" (default) or "inverse". When more than two random terms are specified in the option LinPred, the user can set d

LinPredRandVariance

The option LinPredRandVariance specifies the fixed and random terms for the linear predictor of the random-effect variances for Model="mean". When y~x1+x2+(1|id1)+(1|id2) is specified in the option LinPred, LinPredRandVariance=c(lambda~xx1+(1|id11),

RandDistRandVariance

The option RandDistRandVariance specifies the distributions for the random terms in the LinPredRandVariance. The choice is "gaussian" (default), "gamma", or "inverse-gamma".

LinkRandVariance2

This option specifies the link function for the linear predictor of the variance of random effects, which are specified in the option LinPredRandVariance. The choice is either "log" (default) or "inverse".

LinPredRandVariance2

This option specifies the fixed terms for the linear predictor of the variance of random effects, which is specified in the option LinPredRandVariance. For example, when LinPredRandVariance=c(lambda~xx1+(1|id11),lambda~xx1+(1|id12)) is specified, LinP