• International Journal of Highway Engineering
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• v.14 no.5
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• pp.189-199
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• 2012

PURPOSES: The purpose of this study is to propose a new methodology for developing statistical collision models and to show the validation results of the methodology. METHODS: A new modeling method of introducing variables into the model one by one in a multiplicative form is suggested. A method for choosing explanatory variables to be introduced into the model is explained. A method for determining functional forms for each explanatory variable is introduced as well as a parameter estimating procedure. A model selection method is also dealt with. Finally, the validation results is provided to demonstrate the efficacy of the final models developed using the method suggested in this study. RESULTS: According to the results of the validation for the total and injury collisions, the predictive powers of the models developed using the method suggested in this study were better than those of generalized linear models for the same data. CONCLUSIONS: Using the methodology suggested in this study, we could develop better statistical collision models having better predictive powers. This was because the methodology enabled us to find the relationships between dependant variable and each explanatory variable individually and to find the functional forms for the relationships which can be more likely non-linear.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.431-445
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• 2006

In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.

• The Korean Journal of Applied Statistics
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• v.32 no.4
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• pp.607-618
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• 2019

A new and interesting task in statistics is to effectively analyze functional data that frequently comes from advances in modern science and technology in areas such as meteorology and biomedical sciences. Functional linear regression with scalar response is a popular functional data analysis technique and it is often a common problem to determine a functional association if a functional predictor variable affects the scalar response in the models. Recently, Kong et al. (Journal of Nonparametric Statistics, 28, 813-838, 2016) established classical testing methods for this based on functional principal component analysis (of the functional predictor), that is, the resulting eigenfunctions (as a basis). However, the eigenbasis functions are not generally suitable for regression purpose because they are only concerned with the variability of the functional predictor, not the functional association of interest in testing problems. Additionally, eigenfunctions are to be estimated from data so that estimation errors might be involved in the performance of testing procedures. To circumvent these issues, we propose a testing method based on fixed basis such as B-splines and show that it works well via simulations. It is also illustrated via simulated and real data examples that the proposed testing method provides more effective and intuitive results due to the localization properties of B-splines.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.575-582
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• 2004

We explore the structure and usefulness of CERES plot as a basic tool for dealing with curvature as a function of the new predictor in generalized linear models. If a predictor has a nonlinear effect and there are nonlinear relationships among the predictors, the partial residual plot and augmented partial residual plot are not able to display the correct functional form of the predictor. Unlike these plots, the CERES plot can show the correct form. This is illustrated by simulated data.

• Molecules and Cells
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• v.45 no.7
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• pp.444-453
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• 2022

Multivalent macromolecular interactions underlie dynamic regulation of diverse biological processes in ever-changing cellular states. These interactions often involve binding of multiple proteins to a linear lattice including intrinsically disordered proteins and the chromosomal DNA with many repeating recognition motifs. Quantitative understanding of such multivalent interactions on a linear lattice is crucial for exploring their unique regulatory potentials in the cellular processes. In this review, the distinctive molecular features of the linear lattice system are first discussed with a particular focus on the overlapping nature of potential protein binding sites within a lattice. Then, we introduce two general quantitative frameworks, combinatorial and conditional probability models, dealing with the overlap problem and relating the binding parameters to the experimentally measurable properties of the linear lattice-protein interactions. To this end, we present two specific examples where the quantitative models have been applied and further extended to provide biological insights into specific cellular processes. In the first case, the conditional probability model was extended to highlight the significant impact of nonspecific binding of transcription factors to the chromosomal DNA on gene-specific transcriptional activities. The second case presents the recently developed combinatorial models to unravel the complex organization of target protein binding sites within an intrinsically disordered region (IDR) of a nucleoporin. In particular, these models have suggested a unique function of IDRs as a molecular switch coupling distinct cellular processes. The quantitative models reviewed here are envisioned to further advance for dissection and functional studies of more complex systems including phase-separated biomolecular condensates.

• Journal of the Korean Society of Safety
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• v.24 no.2
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• pp.94-99
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• 2009

This study deals with the traffic accidents at the 3-legged signalized intersections in Cheongu. The goals are to analyze the geometric, traffic and operational conditions of intersections and to develop a various functional forms that predict the accidents. The models are developed through the correlation analysis, the multiple linear, the multiple nonlinear, Poisson and negative binomial regression analysis. In this study, two multiple linear, two multiple nonlinear and two negative binomial regression models were calibrated. These models were all analyzed to be statistically significant. All the models include 2 common variables(traffic volume and lane width) and model-specific variables. These variables are, therefore, evaluated to be critical to the accident reduction of Cheongju.

• Korean Journal of Applied Biomechanics
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• v.28 no.2
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• pp.127-134
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• 2018

Objective: In a statistical linear model estimating the center of rotation of a human hip joint, which is the parameter related to the mean of response vectors, assumptions of homoscedasticity and independence of position vectors measured repeatedly over time in the model result in an inefficient parameter. We, therefore, should take into account the variance-covariance structure of longitudinal responses. The purpose of this study was to estimate the efficient center of rotation vector of the hip joint by using covariance pattern models. Method: The covariance pattern models are used to model various kinds of covariance matrices of error vectors to take into account longitudinal data. The data acquired from functional motions to estimate hip joint center were applied to the models. Results: The results showed that the data were better fitted using various covariance pattern models than the general linear model assuming homoscedasticity and independence. Conclusion: The estimated joint centers of the covariance pattern models showed slight differences from those of the general linear model. The estimated standard errors of the joint center for covariance pattern models showed a large difference with those of the general linear model.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.169-176
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• 2008

We explore the structure and usefulness of three dimensional CERES plot as a basic tool for dealing with curvature as a function of the new predictors in generalized linear models. If predictors have nonlinear effects and there are nonlinear relationships among the predictors, the partial residual plot is not able to display the correct functional form of the predictors. Unlike this plots, the CERES plot can show the correct form. This is illustrated by simulated data.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1169-1178
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• 2010

This article consider a performance model selection based on AIC under unbalanced deign in linear mixed effect models. Vaida and Balanchard (2005) proposed conditional AIC for model selection in linear mixed effect models when the prediction of random effects is of primary interest. Theoretical properties of cAIC and related criteria have been investigated by Liang et al. (2008) and Greven and Kneib (2010). However, all of the simulation studies were performed under a balanced design. Even though functional form of AIC remain same even under the unbalanced deign, it is worthwhile to investigate performance of AIC based model selection criteria under the unbalanced design. The simulation study in this article shows how unbalancedness affects model selection in linear mixed effect models.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.19 no.1
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• pp.71-78
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• 1983

A method is given for obtaining low-order models for a linear time-invariant system of high-order by minimizing a functional of the reduction error between the output response of the original system and the low-order model. The method is based on the Astrom's algorithm for the evaluation of complex integrals and the conjugate gradient method of Fletcher-Reeves. An example illustrating the application of this method is given for approximation of a 4-th order system to be used in the load frequency control of generator systems.