• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.95-102
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• 2017

Gamma generalized linear models have received less attention than Poisson and binomial generalized linear models. Therefore, many old-established statistical techniques are still used in gamma generalized linear models. In particular, existing literature and textbooks still use approximate estimates for the dispersion parameter. In this paper we study the efficiency of various dispersion parameter estimators in gamma generalized linear models and perform numerical simulations. Numerical studies show that the maximum likelihood estimator and Cox-Reid adjusted maximum likelihood estimator are recommended and that approximate estimates should be avoided in practice.

• The Korean Journal of Applied Statistics
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• v.31 no.4
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• pp.475-484
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• 2018

Gamma generalized linear models are useful for non-negative and skewed responses. However, these models have received less attention than Poisson and binomial generalized linear models. In particular, hypothesis testing for the significance of regression coefficients has not been thoroughly studied. In this paper we assess the performance of various test statistics for gamma generalized linear models based on numerical studies. Our results show that the likelihood ratio test and F-type test are generally recommended and that the partial deviance test should be avoided in practice.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.19-25
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• 2001

Random effects models which describe the dependence via random effects in various correlated data have recently received considerable attention in the biomedical literature. They include mixed linear models (MLMs), generatized linear mixed models (GLMMS) and hierarchical generalized linear models (HGLMs). For the inference Lee and Nelder (2000) proposed the first-and second-order REML (restricted maximum likelihood) methods based on hierarchical-likelihood of tee and Welder (1996). In this paper, for Poisson-gamma HGLMs the new methods are theoretically compared with marginal likelihood methods and both methods are illustrated by two practical examples.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• 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.

• The Korean Journal of Applied Statistics
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• v.34 no.5
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• pp.697-710
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• 2021

Relative error prediction is preferred over ordinary prediction methods when relative/percentile errors are regarded as important, especially in econometrics, software engineering and government official statistics. The relative error prediction techniques have been developed in linear/nonlinear regression, nonparametric regression using kernel regression smoother, and stationary time series models. However, random effect models have not been used in relative error prediction. The purpose of this article is to extend relative error prediction to some of generalized linear mixed model (GLMM) with panel data, which is the random effect models based on gamma, lognormal, or inverse gaussian distribution. For better understanding, the real auto insurance data is used to predict the claim size, and the best predictor and the best relative error predictor are comparatively illustrated.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.221-230
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• 2015

Traditionally, sib-pair linkage analysis with repeated measures has employed linear mixed models, but it suffers from the lack of power to find genetic marker loci associated with a phenotype of interest. In this paper, we use a gamma mixed model to improve sib-pair linkage analysis and compare it with a linear mixed model in terms of power and Type I error. We illustrate that the use of gamma mixed model can achieve higher power than linear mixed model with Genetic Analysis Workshop 13 data.

• Journal of the Korea Society of Computer and Information
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• v.27 no.8
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• pp.143-149
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• 2022

Since patent documents contain detailed results of research and development technologies, many studies on various patent analysis methods for effective technology analysis have been conducted. In particular, research on quantitative patent analysis by statistics and machine learning algorithms has been actively conducted recently. The most used patent data in quantitative patent analysis is technology keywords. Most of the existing methods for analyzing the keyword data were models based on the Gaussian probability distribution with random variable on real space from negative infinity to positive infinity. In this paper, we propose a model using gamma probability distribution to analyze the frequency data of patent keywords that can theoretically have values from zero to positive infinity. In addition, in order to determine the regression equation of the gamma-based regression model, two-mode network is constructed to visualize the technological association between keywords. Practical patent data is collected and analyzed for performance evaluation between the proposed method and the existing Gaussian-based analysis models.

• Journal of Preventive Medicine and Public Health
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• v.48 no.3
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• pp.151-169
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• 2015

Objectives: The deleterious effects of air pollution on various health outcomes have been demonstrated. However, few studies have examined the effects of air pollution on liver enzyme levels. Methods: Blood samples were drawn up to three times between 2008 and 2010 from 545 elderly individuals who regularly visited a community welfare center in Seoul, Korea. Data regarding ambient air pollutants (particulate matter ${\leq}2.5{\mu}m$ [$PM_{2.5}$], nitrogen dioxide [$NO_2$], ozone [$O_3$], carbon monoxide, and sulfur dioxide) from monitoring stations were used to estimate air pollution exposure. The effects of the air pollutants on the concentrations of three liver enzymes (aspartate aminotransferase [AST], alanine aminotransferase [ALT], and ${\gamma}$-glutamyltranspeptidase [${\gamma}$-GTP)]) were evaluated using generalized additive and linear mixed models. Results: Interquartile range increases in the concentrations of the pollutants showed significant associations of $PM_{2.5}$ with AST (3.0% increase, p=0.0052), ALT (3.2% increase, p=0.0313), and ${\gamma}$-GTP (5.0% increase, p=0.0051) levels; $NO_2$ with AST (3.5% increase, p=0.0060) and ALT (3.8% increase, p=0.0179) levels; and $O_3$ with ${\gamma}$-GTP (5.3% increase, p=0.0324) levels. Significant modification of these effects by exercise and alcohol consumption was found (p for interaction <0.05). The effects of air pollutants were greater in non-exercisers and heavy drinkers. Conclusions: Short-term exposure to air pollutants such as $PM_{2.5}$, $NO_2$, and $O_3$ is associated with increased liver enzyme levels in the elderly. These adverse effects can be reduced by exercising regularly and abstinence from alcohol.