• Communications for Statistical Applications and Methods
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• v.16 no.6
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• pp.971-978
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• 2009

Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.969-976
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• 2008

Mixed linear models have been widely used in various correlated data including multivariate survival data. In this paper we extend hierarchical-likelihood(h-likelihood) approach for mixed linear models with right censored data to that for left censored data. We also allow a general random-effect structure and propose the estimation procedure. The proposed method is illustrated using a numerical data set and is also compared with marginal likelihood method.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.199-207
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• 2012

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 penalize 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.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.193-200
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• 2000

Modelling the dependence via random effects in censored multivariate survival data has recently received considerable attention in the biomedical literature. The random effects models model not only the conditional survival times but also the conditional hazard rate. Systematic likelihood inference for the models with random effects is possible using Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). The purpose of this presentation is to introduce Ha et al.'s (2000a,b) inferential methods for the random effects models via the h-likelihood, which provide a conceptually simple, numerically efficient and reliable inferential procedures.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1389-1397
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• 2016

Semi-parametric frailty model with nonparametric baseline hazards has been widely used for the analyses of clustered survival-time data. The frailty models can be fitted via an auxiliary Poisson hierarchical generalized linear model (HGLM). For the inferences of the frailty model marginal likelihood, which gives MLE, is often used. The marginal likelihood is usually obtained by integrating out random effects, but it often requires an intractable integration. In this paper, we propose to obtain the MLE via Laplace approximation using a Poisson HGLM approach for semi-parametric frailty model. The proposed HGLM approach uses hierarchical-likelihood (h-likelihood), which avoids integration itself. The proposed method is illustrated using a numerical study.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1209-1216
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• 2015

Competing-risks events are often observed in a clustered clinical study such as a multi-center clinical trial. We propose a joint modelling approach via a shared frailty term for competing risks survival data from a cluster. For the inference we use the hierarchical likelihood (or h-likelihood), which avoids an intractable integration. We derive the corresponding h-likelihood procedure. The proposed method is illustrated via the analysis of a practical data set.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.209-217
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• 2001

We obtain the approximate maximum likelihood estimators (AMLEs) for the scale and location parameters $\theta$ and $\mu$ in the three-parameter Weibull distribution based on Type-II censored samples. We also compare the AMLEs with the modified maximum likelihood estimators (MMLEs) in the sense of the mean squared error (MSE) based on complete sample.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.485-493
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• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1083-1090
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• 2016

In clinical studies, different types of outcomes (e.g. repeated measures data and time-to-event data) for the same subject tend to be observed, and these data can be correlated. For example, a response variable of interest can be measured repeatedly over time on the same subject and at the same time, an event time representing a terminating event is also obtained. Joint modelling using a shared random effect is useful for analyzing these data. Inferences based on marginal likelihood may involve the evaluation of analytically intractable integrations over the random-effect distributions. In this paper we propose a joint HGLM approach for analyzing such outcomes using the HGLM (hierarchical generalized linear model) method based on h-likelihood (i.e. hierarchical likelihood), which avoids these integration itself. The proposed method has been demonstrated using various numerical studies.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1513-1521
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• 2015

Selecting relevant variables for a statistical model is very important in regression analysis. Recently, variable selection methods using a penalized likelihood have been widely studied in various regression models. The main advantage of these methods is that they select important variables and estimate the regression coefficients of the covariates, simultaneously. In this paper, we propose a simple procedure based on a penalized h-likelihood (HL) for variable selection in Poisson hierarchical generalized linear models (HGLMs) for correlated count data. For this we consider three penalty functions (LASSO, SCAD and HL), and derive the corresponding variable-selection procedures. The proposed method is illustrated using a practical example.