DHGLMMODELING {dhglm}

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

Description

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, corr = NULL,
                 spatial = NULL, longitude = NULL, latitude = NULL,
                 spline = NULL, Neighbor = 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, specified as NULL link, is "identity" for Model="mean" and "log" for Model="dispersion".

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 fixed covariates and id1 and id2 as random terms. For Model="dispersion", the main response should be phi, e.g. phi~x1+x2+(1|id1)+(1|id2). This option can specify the model without random effects, e.g., LinPred=phi~x1+x2. The default is "constant", which is set to intercept only the model for the corresponding linear predictors.

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", the choice is "gaussian" (default), "gamma", or "inverse-gamma". When more than one random terms are specified, e.g., y~x1+x2+(1|id1)+(1|id2) in the option LinPred, the different distributions for each random term can be specified, e.g., c("gaussian", "gamma"), which assumes normal distribution for the random term "id1" and gamma distribution for the random term "id2", respectively.

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 Lmatrix=L1+L2, the linear predictor for mu takes X beta + Z1 L1 r1 + Z2 L2 r2, where Z1 and Z2 are the model matrices for the random effects v1=L1 r1 and v2=L2 r2, specified in the option LinPred.

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 different link functions, e.g., LinkRandVariance=c("log","inverse") for each random term.

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),lambda~xx2+(1|id12)) specifies xx1 and xx2 as fixed covariates and id11 and id12 as random terms in the lienar predictors for the variances of the random terms id1 and id2, respectively. For Model="dispersion", the random term is not allowed in the linear predictor of the random-effect variance. The default (NULL) is set to intercept only model for the corresponding linear predictors.

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, LinPredRandVariance2=c(~xxx1,~xxx2) specifies xxx1 and xxx2 as fixed covariates for the linear predictor of random-effect variances for id11 and id12, respectively. The default (NULL) is set to constant variance for the random effects in LinPredRandVariance.

corr

Speicification of correlation structures.

spatial

Speicification of spatial model.

longitude

variable for longitude when spatial option is TRUE.

latitude

variable for latitude when spatial option is TRUE.

spline

option for splince smoothing.

Neighbor

Neiborhood matrix when spatial option is TRUE.

See Also

<dhglmfit>