# Fitting Double Hierarchical Generalized Linear Models using h-likelihood Approach dhglmfit is used to fit a class of double hierarchical generalized linear models (DHGLMs) in which fixed and random effects can be specified in both the mean and the dispersion components. A variety of distributions and link functions for both the response variables and the random effects are allowed. Fixed and random effects can also be fitted in both the mean and the dispersion components. To call the fitting function dhglmfit, models for the mean and dispersion must be specified by DHGLMMODELING object preferably created by calling the DHGLMMODELING function. 2.0 package ```r dhglmfit(RespDist = "gaussian", BinomialDen = NULL, DataMain, MeanModel, DispersionModel, BetaFix = NULL, PhiFix = NULL, LamFix = NULL, mord = 1, dord = 1, REML = TRUE, Maxiter = 200, convergence = 1e-06, EstCorr = FALSE, Dmethod = "deviance") ``` ## Arguments - `RespDist`: The distribution of the response is set by the option RespDist. The user can set it to: "gaussian" (default), "binomial", "poisson", or "gamma". - `BinomialDen`: When RespDist="binomial", one should use the option BinomialDen to specify the denominator for the binomial distribution. This should be "NULL" (default) or a numeric vector of length equal to the length of DataMain. When specified as BinomialDen=NULL and RespDist="binomial", the denominator is 1. - `DataMain`: The option DataMain determines the data frame to be used (non-optional). - `MeanModel`: For the mean model, this option requries DGHLMMODELING object which should specified by the option Model="mean". - `DispersionModel`: For the overdispersion model, this option requries DGHLMMODELING object which should be specified by the option Model="dispersion". - `BetaFix, PhiFix, LamFix`: Three options that determine whether the mean parameters (beta), overdispersion parameters (phi) and random-effect variance (lambda) are to be estimated or maintaned constant. Specifying defaults such as BetaFix=NULL (or PhiFix =NULL or LamFix =NULL) implies that beta (or phi or lambda) is to be estimated. If not, beta (or phi or lambda) is fixed at a value specified by BetaFix (or PhiFix or LamFix). - `mord`: The option mord specifies the order of Laplace approximation to the marginal likelihood for fitting the mean parameters. The choice is either 0 or 1 (default). - `dord`: The option dord specifies the order of Laplace approximation to the adjusted profile likelihood for fitting the dispersion parameters. The choice is either 1 (default) or 2. - `REML`: logical - indicating whether REML method if it is TRUE (default) or ML method if FALSE are used. - `Maxiter`: Maxiter determines the maximum number of iterations for estimating all parameters. The default number is 200 iterations. - `convergence`: Setting this option determines the criterion for convergence, which is computed as the absolute difference between the values of all the estimated parameters in the previous and current iterations. The default criterion is 1e-06. - `EstCorr`: logical - indicating whether correlations are estimated if it is TRUE (default) or not estimated if FALSE are used. - `Dmethod`: Method of fitting dispersion model; "deviance" (default) or "Pearson". ## Examples ```r #### Analysis of crack-growth data #### data(crack_growth) ## GLM ## model_mu<-DHGLMMODELING(Model="mean", Link="log", LinPred=y~crack0) model_phi<-DHGLMMODELING(Model="dispersion") res_glm<-dhglmfit(RespDist="gamma",DataMain=crack_growth, MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) ## JGLM ## model_mu<-DHGLMMODELING(Model="mean", Link="log", LinPred=y~crack0) model_phi<-DHGLMMODELING(Model="dispersion", Link="log", LinPred=phi~cycle) res_jglm<-dhglmfit(RespDist="gamma",DataMain=crack_growth, MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) ## HGLM I ## model_mu<-DHGLMMODELING(Model="mean", Link="log", LinPred=y~crack0+(1|specimen),RandDist="inverse-gamma") model_phi<-DHGLMMODELING(Model="dispersion") res_hglm1<-dhglmfit(RespDist="gamma",DataMain=crack_growth, MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) ## HGLM II ## 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) res_hglm2<-dhglmfit(RespDist="gamma",DataMain=crack_growth, MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) ## DHGLM I ## 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_dhglm1<-dhglmfit(RespDist="gamma",DataMain=crack_growth, MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) #### Analysis of epilepsy data #### data(epilepsy) model_mu<-DHGLMMODELING(Model="mean", Link="log", LinPred=y~B+T+A+T*B+V+(1|patient), RandDist=c("gaussian")) model_phi<-DHGLMMODELING(Model="dispersion") # res_hglm<-dhglmfit(RespDist="poisson",DataMain=epilepsy, # MeanModel=model_mu,DispersionModel=model_phi,Maxiter=1) ```

dhglmfit function