• Communications for Statistical Applications and Methods
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• v.30 no.5
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• pp.437-451
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• 2023

Generalized linear models and generalized linear mixed models (GLMMs) are fundamental tools for predictive analyses. In insurance, GLMMs are particularly important, because they provide not only a tool for prediction but also a theoretical justification for setting premiums. Although thousands of resources are available for introducing GLMMs as a classical and fundamental tool in statistical analysis, few resources seem to be available for the insurance industry. This study targets insurance professionals already familiar with basic actuarial mathematics and explains GLMMs and their linkage with classical actuarial pricing tools, such as the Buhlmann premium method. Focus of the study is mainly on the modeling aspect of GLMMs and their application to pricing, while avoiding technical issues related to statistical estimation, which can be automatically handled by most statistical software.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.353-360
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• 2015

Various statistical models have been proposed over the last decade for spatially correlated Gaussian outcomes. The spatial linear mixed model (SLMM), which incorporates a spatial effect as a random component to the linear model, is the one of the most widely used approaches in various application contexts. Employing link functions, SLMM can be naturally extended to spatial generalized linear mixed model for non-Gaussian outcomes (SGLMM). We review popular SGLMMs on non-Gaussian spatial outcomes and demonstrate their applications with available public data.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.465-474
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• 2015

In this paper, we study the local influence analysis of LIU type estimator in the linear mixed models. Using the method proposed by Shi (1997), the local influence of LIU type estimator in three disturbance models are investigated respectively. Furthermore, we give the generalized Cook's distance to assess the influence, and illustrate the efficiency of the proposed method by example.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.211-223
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• 1999

We propose a simple estimation procedure in the mixed linear models with censored normal data, using both Buckly and James(1979) type pseudo random variables and Lee and Nelder's(1996) estimation procedure. The proposed method is illustrated with the matched pairs data in Pettitt(1986).

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.927-936
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• 2017

To analyze longitudinal count data, Poisson linear mixed models are commonly used. In the models the random effects covariance matrix explains both within-subject variation and serial correlation of repeated count outcomes. When the random effects covariance matrix is assumed to be misspecified, the estimates of covariates effects can be biased. Therefore, we propose reasonable and flexible structures of the covariance matrix using autoregressive and moving average Cholesky decomposition (ARMACD). The ARMACD factors the covariance matrix into generalized autoregressive parameters (GARPs), generalized moving average parameters (GMAPs) and innovation variances (IVs). Positive IVs guarantee the positive-definiteness of the covariance matrix. In this paper, we use the ARMACD to model the random effects covariance matrix in Poisson loglinear mixed models. We analyze epileptic seizure data using our proposed model.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.123-136
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• 2015

Science has developed with great achievements after Galileo's discovery of the law depicting a relationship between observable variables. However, many natural phenomena have been better explained by models including unobservable random effects. A mixed effect model was the first statistical model that included unobservable random effects. The importance of the mixed effect models is growing along with the advancement of computational technologies to infer complicated phenomena; subsequently mixed effect models have extended to various statistical models such as hierarchical generalized linear models. Hierarchical likelihood has been suggested to estimate unobservable random effects. Our special issue about mixed effect models shows how they can be used in statistical problems as well as discusses important needs for future developments. Frequentist and Bayesian approaches are also investigated.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.761-770
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• 2012

We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.423-433
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• 2014

Test statistics using cumulative sums of residuals have been widely used in various regression models including generalized linear models(GLM). Recently, Pan and Lin (2005) extended this testing procedure to the generalized linear mixed models(GLMM) having random effects, in which we encounter difficulties in computing the marginal likelihood that is expressed as an integral of random effects distribution. The Gaussian quadrature algorithm is commonly used to approximate the marginal likelihood. Many commercial statistical packages provide an option to apply this type of goodness-of-fit test in GLMs but available programs are very rare for GLMMs. We suggest a computational algorithm to implement the testing procedure in GLMMs by a freely accessible R package, and also illustrate through practical examples.

• Proceedings of the Safety Management and Science Conference
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• 2009.04a
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• pp.185-192
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• 2009

The research contributes extending and reviewing of restricted (constrained) and unrestricted (unconstrained) models in GLM(Generalized Linear Models). The paper includes the methodology for finding EMS(Expected Mean Square) and $F_0$ ratio. The results can be applied to the gauge R&R(Reproducibility and Repeatability) in MSA(Measurement System Analysis).

• The Korean Journal of Applied Statistics
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• v.17 no.2
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• pp.337-346
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• 2004

The Pearson chi-square goodness-of-fit test and the likelihood ratio tests are usually used for testing independence in two-way contingency tables under random sampling. But both of these tests may provide false results for the contingency table with clustered observations. In this case we consider the generalized linear mixed model which includes random effects of clustering in addition to the fixed effects of covariates. Both the heterogeneity between clusters and the dependency within a cluster can be explained via generalized linear mixed model. In this paper we introduce several types of generalized linear mixed model for testing independence in contingency tables with clustered observations. We also discuss the fitting of these models through a real dataset.