Earticle

The study focuses on the Repeated Measurements Design (RMD) which observations are periodically made for identical subjects within definite time periods. One of the purposes of this design is to monitor and keep track of replicated records within regular period over years. This paper also presents the classification models of RMD that is developed according to the number of factors in Between-Subject (BS) variates and Within-Subject (WS) variates. The types of models belong to each number of factors: One factor is 0BS 1WS. Two factors are 1BS 1WS and 0BS 2WS. Three factors are 1BS 2WS and 2BS 1WS. Lastly, the four factors include model of 2BS 2WS In addition, the study explains the generation mechanism of models for RMD using Generalizability Design (GD). GD is a useful method for practitioners to identify linear model of experimental design, since it generates a Venn diagram. Lastly, the research develops three types of 1BS 2WS RMDs with crossed factors and nested factors. Those are random models, mixed models and fixed models and they are presented by using Generalizability Design,(S:AxB)xC . Moreover, the example of applications and its implementation steps of models developed in the study are presented for better comprehension.

This paper examined different 2-parameter and 3-parmeter nonlinear models for height-diameter prediction that incorporated different stands variable for the development of robust generalised height-diameter models. Stratified random sampling was employed in selecting 54 sample plots (20 m by 20 m) for six different age series (6, 9, 13, 15, 17 and 21 years old) plantation. Diameter at breast height (D), total height (h) and merchantable height (hm) for individual trees with D≥10 cm were measured. The Nonlinear model forms were fitted by ordinary nonlinear least square (ONLS) regression to select the base model without random parameters. Stands variables where then incorporated as random components for mixed-effects modelling using Gauss-Newton algorithm for nonlinear (weighted) least-squares. The best models were adjured using Standard error of estimate (SEE), Root means square (RMSE) and Akaike’s Information Criterion (AIC) and validated by Z-Score values and residual plot. The overall best height-diameter prediction equation for 2-parameter and 3-parameter estimate was Meyer function and Logistic models respectively. All the parameters of the models predicted at p＜0.05 are significant justifying the use of this model for future predictions in the study area expect for Prodan model. The nonlinear mixed effects yield model developed are efficient and biologically logical in predicting yield of teak in the study area, therefore enabling forest managers to optimise harvest planning, plantation regeneration and management in Area J4 of Omo Forest Reserve.

Objectives: Using atmospheric dispersion representative models (AERMOD and CALPUFF), the emissions characteristics of each model were compared and analyzed in ready-mixed concrete manufacturing facilities that generate a large amount of particulate matter (PM-10, PM-2.5). Methods: The target facilities were the ready-mixed concrete manufacturing facilities (Siheung RMC, Goyang RMC, Ganggin RMC) and modeling for each facility was performed by dividing it into construction and operation times. The predicted points for each target facility were selected as 8-12ea (Siheung RMC 10, Goyang RMC 8, and Gangjin RMC 12ea) based on an area within a two-kilometer radius of each project district. The terrain input data was SRTM-3 (January-December 2019). The meteorological input data was divided into surface weather and upper layer weather data, and weather data near the same facility as the target facility was used. The predicted results were presented as a 24-hour average concentration and an annual average concentration. Results: First, overall, CALPUFF showed a tendency to predict higher concentrations than AERMOD. Second, there was almost no difference in the concentration between the two models in non-complex terrain such as in mountainous areas, but in complex terrain, CALPUFF predicted higher concentrations than AERMOD. This is believed to be because CALPUFF better reflected topographic characteristics. Third, both CALPUFF and AERMOD predicted lower concentrations during operation (85.2-99.7%) than during construction, and annual average concentrations (76.4-99.9%) lower than those at 24 hours. Fourth, in the ready-mixed concrete manufacturing facility, PM-10 concentration (about 40 ㎍/m³) was predicted to be higher than PM-2.5 (about 24 ㎍/m³). Conclusions: In complex terrain such as mountainous areas, CALPUFF predicted higher concentrations than AERMOD, which is thought to be because CALPUFF better reflected topographic characteristics. In the future, it is recommended that CALPUFF be used in complex terrain and AERMOD be used in other areas to save modeling time. In a ready-mixed concrete facility, PM-10, which has a relatively large particle size, is generated more than PM-2.5 due to the raw materials used and manufacturing characteristics.

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 F0 ratio. The results can be applied to the gauge R&R(Reproducibility and Repeatability) in MSA(Measurement System Analysis).

현대 스포츠 경기는 신체적·기술적 경쟁을 넘어 심리적, 전술적, 환경적 요인을 포함하는 복잡하고 고도화된 체제 로 변화하였다. 이에 따라 경기력 분석은 코칭 및 전략 의사 결정의 과학적 근거를 제공하는 핵심 수단으로 중요성이 증대 됨에 따라 분석 목적과 데이터의 구조에 따른 다양한 통계 모형이 적용되고 있다. 이에 이 연구는 스포츠 경기력 예측에서 가장 많이 적용되어 왔던 로지스틱 회귀모형(Logistic Regression Model, LRM)과 비선형 및 종속성 반영이 가능한 일반화 가법 혼합모형(Generalized Additive Mixed Model, GAMM)을 동일한 KBL 경기 데이터를 적용하여 그 결과를 비교·분석함으로써 적절성을 논의하였다. 분석 결과 LRM은 해석 용이성과 안정적 추정치를 제공하며 주요 변수의 유의 성이 명확하게 파악되었으나, 종속성과 비선형성 가정을 완전히 충족하지 못해 통계적 추론의 신뢰도가 다소 제한적이었 다. 반면 GAMM은 평활 함수를 통한 비선형 효과 포착과 무작위 효과를 통한 팀 및 선수 수준의 종속성 반영으로 예측력 및 설명력이 소폭 향상되었으나, 복잡성 증가에 따른 추정치 불확실성 확대가 동시에 관찰되었다. 결론적으로 통계적 모형의 선택은 스포츠 데이터 특성의 반영이 중요하며, 예측 및 설명 목적에 따라 LRM과 GAMM의 통합적 활용 전략이 효과적임을 시사한다.

Modern sports competition has evolved into a complex system involving physical, technical, psychological, tactical, and environmental factors. Performance analysis has thus become essential for providing scientific evidence to support coaching and strategic decisions. This study compares Logistic Regression Models(LRM) and Generalized Additive Mixed Models(GAMM) using Korean Basketball League data. LRM offers interpretability and stable estimates but is limited by assumptions of linearity and independence. GAMM addresses these limitations by incorporating smoothing functions and random effects to model nonlinear relationships and data dependencies, leading to slightly improved prediction and explanation. However, GAMM’s complexity increases estimation uncertainty. The results highlight the importance of selecting statistical models aligned with data characteristics and suggest an integrated approach using LRM for interpretive clarity and GAMM for enhanced predictive accuracy. This complementary strategy advances the rigor and utility of sports performance modeling.

Purpose: This study analyzed four-year data (2021~2024) on cardiovascular disease risk among workers in a manufacturing factory, using generalized estimating equations (GEE) and linear mixed-effects models to examine temporal changes and identify factors influencing cardiovascular disease (CVD) risk. Methods: The study included 546 participants who underwent health examinations in March and September each year from 2021 to 2024. CVD risk was assessed using physical examination results. Data were analyzed with R 4.5.1 (R Foundation for Statistical Computing, Vienna, Austria) and SPSS/WIN 25.0. Results: Time-effect analysis of CVD risk components showed that systolic blood pressure significantly increased over time (β=.84, p<.001), while diastolic blood pressure significantly decreased (β=-.46, p=.004). Body mass index (BMI) also significantly increased (β=.11, p=.002). In the GEE logistic regression analysis, Male workers had 2.38 times higher odds of being in the high-risk group compared to females (OR=2.38, p=.009). Higher systolic blood pressure (OR=2.52, p<.001) and fasting blood glucose (OR=8.66, p<.001) were significant predictors of high CVD risk. Conclusion: When developing and implementing workplace interventions to reduce CVD risk among manufacturing workers, key predictors such as sex, blood pressure, and blood glucose should be considered for effective risk stratification and targeted prevention. This study is important because it examined both temporal changes and influencing factors of CVD risk using four-year longitudinal data.

Despite the success of recent genome-wide association studies investigating longitudinal traits, a large fraction of overall heritability remains unexplained. This suggests that some of the missing heritability may be accounted for by gene-gene and gene-time/environment interactions. In this paper, we develop a Bayesian variable selection method for longitudinal genetic data based on mixed models. The method jointly models the main effects and interactions of all candidate genetic variants and non-genetic factors and has higher statistical power than previous approaches. To account for the within-subject dependence structure, we propose a grid-based approach that models only one fixed-dimensional covariance matrix, which is thus applicable to data where subjects have different numbers of time points. We provide the theoretical basis of our Bayesian method and then illustrate its performance using data from the 1000 Genome Project with various simulation settings. Several simulation studies show that our multivariate method increases the statistical power compared to the corresponding univariate method and can detect gene-time/ environment interactions well. We further evaluate our method with different numbers of individuals, variants, and causal variants, as well as different trait-heritability, and conclude that our method performs reasonably well with various simulation settings.

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.

Longitudinal studies repeatedly measure outcomes over time. Therefore, repeated measurements are serially correlated from same subject (within-subject variation) and there is also variation between subjects (between-subject variation). The serial correlation and the between-subject variation must be taken into account to make proper inference on covariate effects (Diggle et al., 2002). However, estimation of the covariance matrix is challenging because of many parameters and positive definiteness of the matrix. To overcome these limitations, we propose autoregressive moving average Cholesky decomposition (ARMACD) for the linear mixed models. The ARMACD allows a class of flexible, nonstationary, and heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the random effects covariance matrix. We analyze a real dataset to illustrate our proposed methods.

Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

Mixed models are frequently used in inference for the repeated measurement data of biological and biomedical studies. In this paper, we consider the efficiency of the estimated generalized least squares estimator for the linear mixed model. We find that it works well with respect to consistency and empirical efficiency and has similar precision with the generalized least squares estimator. For the nonlinear mixed model, we notice that the approximate extended least squares estimator based on linearization may have serious bias in mean parameter estimates, especially when the variability in random coefficients is large. On the other hand, the extended least squares estimator using Monte Carlo method produces estimates close to that of exact extended least squares estimator and both procedures yield good estimates and confidence intervals for the mean parameters.

Maximum likelihood estimator (MLE) and restricted maximum likelihood estimator (REMLE) approaches are available in analyzing the linear mixed model (LMM) like bioequivalence trials. US FDA (2001) guides that REMLE may be useful to assess bioequivalence (BE) test. This paper studies the statistical behaviors of the methods in assessing BE tests when some of observations are missing at random. The simulation results show that the REMLE maintains the given nominal level well and the MLE gives a bit higher power. Considering the levels and the powers, the REMLE approach is recommended when the sample sizes are small to moderate and the MLE approach should be used when the sample size is greater than 30.

Standard estimation methods for linear mixed models are sensitive to influential observations. However, tools and concepts for linear mixed model diagnostics are rudimentary until now and research is heavily demanded in linear mixed models. In this paper, we consider two diagnostics to evaluate the effects of individual observations in the estimation of fixed effects for linear mixed models. Those are Cook's distance and COVRATIO. Results of our limited simulation study suggest that the Cook's distance is not good statistical quantity in linear mixed models. Also calibration point for COVRATIO seems to be quite conservative.

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.

The teat number of a sow plays an important role for weaning pigs and has been utilized in selection of swine breeding stock. Various linear models have been employed for genetic analyses of teat number although the teat number can be considered as a count trait. Theoretically, Poisson error mixed models are more appropriate for count traits than Normal error mixed models. In this study, the two models were compared by analyzing data simulated with Poisson error. Considering the mean square errors and correlation coefficients between observed and fitted values, the Poisson generalized linear mixed model (PGLMM) fit the data better than the Normal error mixed model. Also these two models were applied to analyzing teat numbers in four breeds of swine (Landrace, Yorkshire, crossbred of Landrace and Yorkshire, crossbred of Landrace, Yorkshire, and Chinese indigenous Min pig) collected in China. However, when analyzed with the field data, the Normal error mixed model, on the contrary, fit better for all the breeds than the PGLMM. The results from both simulated and field data indicate that teat numbers of swine might not have variance equal to mean and thus not have a Poisson distribution.

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 likelihood-based inference in a nonlinear generalized mixed model often requires computing moments of truncated multivariate normal random variables. Many methods have been proposed for the computation using a recurrence relation or the moment generating function; however, these methods rely on high dimensional numerical integrations. The numerical method is known to be inefficient for high dimensional integral in accuracy. Besides the accuracy, the methods demand too much computing time to use them in practical analyses. In this note, a moment calculation method is proposed under an assumption of a certain covariance structure that occurred mostly in generalized mixed models. The method needs only low dimensional numerical integrations.

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components in the mixed model is developed. This computing algorithm which used W-matrix saves both storage usage and computing time.