dhglm-package: Double Hierarchical Genearlized Linear Models

In dhglm: Double Hierarchical Generalized Linear Models

Description

The dhglm package is used to fit double hierarchical generalized linear models (DHGLMs) in which random effects can be specified in both the mean and the dispersion components (Lee and Nelder, 2006; Lee, Nelder, and Pawitan, 2006). It can also be used to fit generalized linear models (GLMs) of Nedler and Wedderburn (1972), joint GLMs of Nelder and Lee (1991), and hierarchical GLMs (HGLMs) of Lee and Nelder (1996, 2001). Dispersion parameters of the random effects in the mean model can also be modeled with random effects (Noh, Lee and Pawitan, 2005). The response variable is allowed to follow a Gaussain, binomial, Poisson, or gamma distribution. The distribution of random effects can be specified as Gaussian, gamma, inverse-gamma or beta. It can handle complex structures such as crossed or nested designs in which various combinations of different distributions for random effects can be specified. Fixed effects in the mean can be estimated by maximizing the h-likelihood or a first-order Laplace approximation to the marginal likelihood. Dispersion parameters are estimated by using first-order adjusted profile likelihood, an extension of the restricted maximum likelihood; alternatively, these parameters can be assigned fixed values. The dhglm package also produces model-checking plots for various component of the model.

Details

Package:	dhglm
Type:	Package
Version:	1.6
Date:	2016-09-19
License:	Unlimited
LazyLoad:	yes

This is version 1.6 of the dhglm package.

Author(s)

Manegseok Noh, Youngjo Lee

Maintainer: Maengseok Noh <[e-mail]>

References

Lee, Y. and Nelder, J. A. (1996). Hierarchical generalised linear models (with discussion), Journal of the Royal Statistical Society B, 58, 619–678.

Lee, Y. and Nelder, J. A. (2001). Hierarchical generalised linear models : A synthesis of generalised linear models, random-effect model and structured dispersion, Biometrika, 88, 987–1006.

Lee, Y. and Nelder, J. A. (2006). Double hierarchical generalized linear models (with discussion), Applied Statistics 55, 139–185.

Lee, Y. Nelder, J. A. and Pawitan, Y. (2006). Generalised linear models with random effects: unified analysis via h-likelihood. Chapman & Hall: London.

Nelder, J. A. and Lee, Y. (1991). Generalised linear models for the analysis of Taguchi-type experiments, Applied Stochastic Models and Data Analysis, 7, 107–120.

Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalised linear models, Journal of the Royal Statistical Society A, 135, 370–384.

Noh, M., Lee, Y. and Pawitan, Y. (2005). Robust ascertainment-adjusted parameter estimation, Genetic Epidemiology, 29, 68–75.

See Also

<dhglmfit>

Examples

### DHGLM introducing random effects in the overdispersion for crack growth data
data(crack_growth)
model_mu<-DHGLMMODELING(Model="mean", Link="log", LinPred=y~crack0+(1|specimen),
RandDist="inverse-gamma")
model_phi<-DHGLMMODELING(Model="dispersion", Link="log", 
LinPred=phi~cycle+(1|specimen), RandDist="gaussian")
res_crack<-dhglmfit(RespDist="gamma",DataMain=crack_growth,
MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1)

Example output

Loading required package: Matrix
Loading required package: boot
Loading required package: MASS
Loading required package: car
Loading required package: carData

Attaching package: 'car'

The following object is masked from 'package:boot':

    logit

Loading required package: sandwich
Distribution of Main Response :  
                         "gamma" 
[1] "Estimates from the model(mu)"
y ~ crack0 + (1 | specimen)
[1] "log"
            Estimate Std. Error t-value
(Intercept)   -5.688     0.4585 -12.405
crack0         2.397     0.3852   6.222
[1] "Estimates for logarithm of lambda=var(u_mu)"
[1] "inverse-gamma"
         Estimate Std. Error t-value
specimen   -3.332     0.3443  -9.677
[1] "Estimates from the model(phi)"
phi ~ cycle + (1 | specimen)
[1] "log"
            Estimate Std. Error t-value
(Intercept)   -2.879     0.1728 -16.657
cycle         -9.052     2.2202  -4.077
[1] "Estimates for logarithm of var(u_phi)"
         Estimate Std. Error t-value
specimen   -2.101      0.803  -2.617
[1] "========== Likelihood Function Values and Condition AIC =========="
                                                         [,1]
-2ML (-2 p_v(mu),v(phi) (h))          :            -1578.2292
-2RL (-2 p_beta(mu),v(mu),beta(phi),v(phi) (h)) :  -1576.3655
cAIC                           :                   -1540.1652
Scaled Deviance                :                     222.1321
df                             :                     222.1321

dhglm documentation built on May 2, 2019, 2:08 a.m.