Double Hierarchical Generalized Linear Models (With Discussion)

Lee, Youngjo; Nelder, J. A.

doi:10.1111/j.1467-9876.2006.00538.x

Cited by 311 publications

(587 citation statements)

References 134 publications

(201 reference statements)

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“…The square matrix of left-hand side of (3.4) is the negative Hessian matrix, H * = −∂ 2 h * /∂τ 2 , leading to an asymptotic variance of β (Lee and Nelder, 1996;Ha and Lee, 2003):…”

Section: Standard Estimation Proceduresmentioning

confidence: 99%

“…For this we use the SCAD penalty. The h-likelihood (or hierarchical likelihood; Lee and Nelder, 1996) avoids such intractable integration and provides a statistically efficient procedure in random-effect models such as hierarchical GLMs (HGLMs; Lee and Nelder, 1996;Ha, 2008;Kim et al, 2011) and frailty models (Lee et al, 2006;Ha et al, 2010). The proposed method is illustrated using simulation studies and a well-known survival data, i.e.…”

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confidence: 99%

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H-likelihood approach for variable selection in gamma frailty models

Cho²

2012

Journal of the Korean Data and Information Science Society

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Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalized h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.

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“…The square matrix of left-hand side of (3.4) is the negative Hessian matrix, H * = −∂ 2 h * /∂τ 2 , leading to an asymptotic variance of β (Lee and Nelder, 1996;Ha and Lee, 2003):…”

Section: Standard Estimation Proceduresmentioning

confidence: 99%

mentioning

confidence: 99%

H-likelihood approach for variable selection in gamma frailty models

Cho²

2012

Journal of the Korean Data and Information Science Society

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“…Lee and Nelder [1996] developed a systematic likelihood inference for HGLMs by using the h-likelihood. By eliminating some of the parameters from the h-likelihood, we can have two forms of profile likelihoods: (1) the classical marginal likelihood, and (2) the adjusted profile likelihood.…”

Section: H-likelihood Proceduresmentioning

confidence: 99%

“…Lee and Nelder [1996] observed that although in general a joint maximization of h-likelihood does not provide marginal MLEs for b, the deviance differences constructed from h and p b (h) are often very similar, so that they proposed using h for estimating b. However, with sparse binary data, the use of h for estimating b results in a nonignorable bias.…”

Section: H-likelihood Proceduresmentioning

confidence: 99%

“…A computational method to correct the bias of PQL is given in Pawitan [2000], but the method does not work for small cluster sizes. For GLMMs, the h-likelihood of Lee and Nelder [1996] allows estimation of fixed regression estimates together with the random-effect estimates directly, without the need of integration to find the marginal likelihood. The PQL method is similar to this h-likelihood method, but it ignores some derivative terms in the dispersion estimation, causing nonignorable biases [Lee and Nelder, 2001].…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent variance estimation for binary traits in family‐based studies

Noh

Yip

Lee

et al. 2005

Genetic Epidemiology

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In biometrical genetic analyses of binary traits, the use of family data overcomes some limitations of twin studies, particularly in terms of sample size and types of genetic or environmental factors that can be estimated. However, because of computational problems, recent methods in the application of generalized linear mixed models for family data structure have limited the ability to handle large data sets with general covariates. In this paper, we investigate the use of the hierarchical likelihood approach to the analysis of binary traits from family data. In a simulation study, the method is shown to be highly accurate for the estimation of both the variance components and fixed regression parameters, even for small family sizes. For illustration, we analyze a real data set of familial aggregation of preeclampsia, a pregnancy-induced hypertension. When possible, the analysis is compared with the exact maximum likelihood approach. Genet. Epidemiol. 30: 37-47, 2006. r 2005 Wiley-Liss, Inc.

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Generalized Linear Models

Jørgensen¹

2001

Encyclopedia of Environmetrics

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Generalized linear models provide a general framework for handling regression modeling for normal and non-normal data, including multiple linear regression, ANOVA, logistic regression, Poisson regression and log-linear models for contingency tables. All the major statistical packages include facilities for tting generalized linear models. A generalized linear model is de ned by choosing a link function and a variance function, along with choosing a response variable and a set of explanatory variables. The link function transforms the mean of the response variable to a scale where the model is linear. The variance function describes how the variance behaves as a function of the mean. Each choice of variance function corresponds to a certain deviance function, and model tting is accomplished by minimizing the deviance, generalizing least squares tting. Inference on parameters, and hypothesis testing is performed by means of analysis of deviance, generalization the classical ANOVA method. Estimation and analysis of deviance are based on quasi-likelihood methods, 1 requiring only second-moment assumptions, thereby providing a certain robustness against misspeci cation of the probability model. The choice of link and variance functions may be checked by means of residual analysis.

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Double Hierarchical Generalized Linear Models (With Discussion)

Cited by 311 publications

References 134 publications

H-likelihood approach for variable selection in gamma frailty models

H-likelihood approach for variable selection in gamma frailty models

Multicomponent variance estimation for binary traits in family‐based studies

Generalized Linear Models

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