• Journal of the Korean Data and Information Science Society
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• 제20권2호
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• pp.445-452
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• 2009

Credibility models are actuarial tools to distribute premiums fairly among a heterogeneous group of policyholders. Many existing credibility models can be expressed as special cases of linear mixed effects models. In this paper we propose a nonlinear credibility regression model by reforming the linear mixed effects model through kernel machine. The proposed model can be seen as prediction method applicable in any setting where repeated measures are made for subjects with different risk levels. Experimental results are then presented which indicate the performance of the proposed estimating procedure.

• Journal of the Korean Statistical Society
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• 제28권3호
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• pp.311-324
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• 1999

The problem of 'outliers', observations which look suspicious in some way, has long been one of the most concern in the statistical structure to experimenters and data analysts. We propose a model for an outlier problem and also analyze it in linear regression model using a Bayesian approach. Then we use the mean-shift model and SSVS(George and McCulloch, 1993)'s idea which is based on the data augmentation method. The advantage of proposed method is to find a subset of data which is most suspicious in the given model by the posterior probability. The MCMC method(Gibbs sampler) can be used to overcome the complicated Bayesian computation. Finally, a proposed method is applied to a simulated data and a real data.

• Journal of the Korean Data and Information Science Society
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• 제23권4호
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• pp.749-756
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• 2012

소지역 추정을 위해 널리 사용되고 있는 방법 중 하나는 선형혼합효과모형이다. 그러나 종속변수와 독립변수 사이의 관계가 비선형일 때 이 모형은 소지역 관련 모수에 대해 편의된 추정값을 초래한다. 본 논문에서는 M-분위수 커널회귀를 사용하여 소지역의 평균을 추정하는 방법을 제안한다. 그리고 모의실험을 통하여 서포트벡터분위수회귀와 성능을 비교함으로써 제안된 방법의 우수성을 보인다.

• 응용통계연구
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• 제30권6호
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• pp.957-981
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• 2017

관측되지 않는 효과 또는 고정효과로 설명할 수 없는 분산 구조가 포함되어 정확한 모수 추정이 어려운 경우 체계적인 분석을 위해 일반화 선형 모형은 임의효과가 포함된 일반화 선형 혼합 모형으로 확장되었다. 본 연구에서는 일반화 선형 모형 중에서도 이분적인 반응변수를 다루는 로지스틱 회귀모형에 임의효과를 포함한 최대 우도 추정 방법을 설명한다. 그중에서도 라플라스 근사법, 가우스-에르미트 구적법, 적응 가우스-에르미트 구적법 그리고 유사가능도 우도에 대한 최대우도 추정법을 자세히 알아본다. 또한 제안한 방법을 사용하여 한국 복지 패널 데이터에서 정신건강과 생활만족도가 자원봉사활동에 미치는 영향에 대해 분석한다.

• Journal of the Korean Statistical Society
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• 제28권2호
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• pp.225-234
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• 1999

We consider the following semi-parametric non-linear mixed effect regression model : y\ulcorner=f($\chi$\ulcorner;$\beta$)+$\sigma$$\mu$($\chi$\ulcorner)+$\sigma$$\varepsilon$\ulcorner,i=1,…,n,y*=f($\chi$;$\beta$)+$\sigma$$\mu$($\chi$) where y'=(y\ulcorner,…,y\ulcorner) is a vector of n observations, y* is an unobserved new random variable of interest, f($\chi$;$\beta$) represents fixed effect of known functional form containing unknown parameter vector $\beta$\ulcorner=($\beta$$_1$,…,$\beta$\ulcorner), $\mu$($\chi$) is a random function of mean zero and the known covariance function r(.,.), $\varepsilon$'=($\varepsilon$$_1$,…,$\varepsilon$\ulcorner) is the set of uncorrelated measurement errors with zero mean and unit variance and $\sigma$ is an unknown dispersion(scale) parameter. On the basis of finite-sample, small-dispersion asymptotic framework, we derive an absolute lower bound for the asymptotic mean squared errors of prediction(AMSEP) of the regular-consistent non-linear predictors of the new random variable of interest y*. Then we construct an optimal predictor of y* which attains the lower bound irrespective of types of distributions of random effect $\mu$(.) and measurement errors $\varepsilon$.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.941-949
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• 2014

Unit level logistic regression model with mixed effects has been used for estimating small area proportions, which treats the spatial effects as random effects and assumes linearity between the logistic link and the covariates. However, when the functional form of the relationship between the logistic link and the covariates is not linear, it may lead to biased estimators of the small area proportions. In this paper, we relax the linearity assumption and propose two types of kernel-based logistic regression models for estimating small area proportions. We also demonstrate the efficiency of our propose models using simulated data and real data.

• Communications for Statistical Applications and Methods
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• 제21권5호
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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.

• Journal of the Korean Data and Information Science Society
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• 제14권1호
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• pp.131-141
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• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• Journal of Preventive Medicine and Public Health
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• 제24권1호
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• pp.29-36
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• 1991

A multiple regression analysis using ordinary least square (OLS) is frequently used for the projection of health expenditure as well as for the identification of factors affecting health care costs. Data for the analysis often have mixed characteristics of time series and cross section. Parameters as a result of OLS estimation, in this case, are no longer the best linear unbiased estimators (BLUE) because the data do not satisfy basic assumptions of regression analysis. The study theoretically examined statistical problems induced when OLS estimation was applied with the time series cross section data. Then both the OLS regression and time series cross section regression (TSCS regression) were applied to the same empirical da. Finally, the difference in parameters between the two estimations were explained through residual analysis.

• Asian-Australasian Journal of Animal Sciences
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• 제13권12호
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• pp.1691-1698
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• 2000

An in situ digestion trial (Experiment 1) and a lactation trial (Experiment 2) were conducted to determine the effects of replacing corn and wheat bran with soyhulls (SH) in lactating dairy cow diets on the extent and kinetics of digestion of DM and NDF, and lactation performance. In experiment 1, five mixed feeds consisting of mixed concentrate and roughages (50:50 on a DM basis) were formulated on isonitrogenous and isoenergetic bases to produce five levels (0, 25, 50, 75 and 100%) of SH replacement for corn and wheat bran. SH had high in situ digestion (92 and 89% for potentially digestible DM and NDF) and fairly fast digestion rate (7.2 and 6.3 %/h for DM and NDF). Increasing level of SH replacement resulted in increased NDF digestibility (linear, p=0.001-0.04) and similar DM digestibility (beyond 12 h incubation, p=0.10-0.41). As level of SH replacement increased, percentage of slowly digestible fraction (b) of DM increased (linear, p=0.03), percentage of rapidly digestible fraction (a) of DM tended to decrease (linear, p=0.14), and DM digestion lag time tended to be longer (linear, p=0.13). Percentage of potentially digestible fraction (a+b) and digestion rate (c) of slowly digestible fraction of dietary DM remained unaltered (p=0.36-0.90) with increasing SH in the diet. Increasing level of SH for replacing corn and wheat bran in the diet resulted in increases in percentages of b (quadratic, p<0.001), a (linear, p=0.08), a+b (quadratic, p=0.001) and a tendency to increase in c for NDF (linear, p<0.19). It was also observed that there was a satisfactory fit of a non-linear regression model to NDF digestion data ($R^2=0.986-0.998$), but a relatively poor fit of the model to DM digestion data ($R^2=0.915-0.968$). In experiment 2, 42 lactating Holstein cows were used in a randomized complete block design. SH replaced corn and wheat bran in mixed concentrates at 0, 25, and 50%, respectively. These mixed concentrates were mixed with roughages and fed ad libitum as complete diets. Replacing corn and wheat bran with SH at 0, 25 and 50% levels did not influence (p=0.56-0.95) DM intakes (18.4, 18.6, and 18.5 kg/d), milk yields (27.7, 28.4 and 27.6 kg/d), 4% fat-corrected-milk (FCM) yields (26.2, 27.6, and 27.3 kg/d) and percentages of milk protein (3.12, 3.17 and 3.18%), milk lactose (4.69, 4.76 and 4.68%) and SNF (8.50, 8.64, and 8.54%). On the other hand, milk fat percentges linearly increased (3.63, 3.85 and 3.90% for SH replacement rates of 0, 25 and 50% in the diet, p=0.08), while feed costs per kg FCM production were reduced.