회귀그래픽 방법을 이용한 로지스틱 회귀모형 분석

이학배 한국자료분석학회 2005 Journal of the Korean Data Analysis Society Vol.7 No.3

Regression graphics based on dimension reduction has been discussed for the decade. Regression graphics approach in the logistic regression will be explored. The main issue of regression graphics focuses on estimating the central subspace. With respect of regression graphics, dimension reduction is enough to find regression model with low-dimensional predictors from originally high-dimensional predictors without losing original information of the regression model. This paper discusses regression graphics based on dimension reduction about selection procedure of predictors in a sense. Regression graphics based on dimension reduction suggests some linear combination of original predictors as predictors of logistic regression model. 차원축소에 기초한 회귀그래픽 방법은 최근 몇 년간 많은 논의가 있어 왔다. 로지스틱 회귀모형의 분석 시 기존의 접근 방법과 더불어 회귀그래픽 방법에 관하여 논의 하고자 한다. 차원축소에 기초한 회귀그래픽 방법은 차원축소를 위해 설명변수들이 형성하는 중심부공간을 추정하는 문제를 기본 개념으로 시작한다. 차원축소는 회귀 그래픽 방법론의 관점에서 설명하면 원래 고차원의 그래픽으로 설명되어야 할 설명변수의 회귀모형이 원래의 모든 정보를 잃어버림 없이 축소된 저차원 그래픽의 설명변수를 가진 회귀모형으로 요약해도 충분하다는 것이다. 본 논문은 로지스틱 회귀 모형의 변수 선택의 주제에 대하여 차원축소에 기초한 회귀그래픽 방법을 이용하여 논의하고자 한다. 차원축소에 기초한 회귀그래픽 방법은 로지스틱 회귀모형의 변수를 원래 변수들의 선형적 결합들로 제시한다.

한계모형 산점도를 이용한 회귀모형 적절성 평가

이학배 한국자료분석학회 2004 Journal of the Korean Data Analysis Society Vol.6 No.3

Scatterplots of residuals against fitted values, predictors or others are used as a tool for checking deficiencies of regression model. Residual scatterplot may not be appropriate for nonlinear regression. Marginal model plots based on marginal model checking condition are explored as a method to investigate adequacy of regression model. Marginal checking conditions show that all information full model includes can be explained by all marginal models. Regression can be regarded as exploring unknown conditional distribution of conditional random variable . This paper investigates the regression function and the variance function because regression function and variance function characterize basic properties of regression model. Lowess smoother of fit estimated from the model are compared with lowess smoother based on the observed data. 일반적으로 고려하는 잔차 산점도는 회귀모형의 부적절성을 점검하는 도구로서 널리 사용되고 있다. 잔차 산점도는 비선형 회귀모형을 분석할 때 비효율적이다. 본 논문에서는 회귀모형의 적절성을 조사하기 위하여 잔차 산점도가 아닌 한계 모형 점검 조건에 기초한 한계 모형 산점도를 논의한다. 한계 모형 점검 조건은 전체모형이 내포하는 모든 것을 모든 한계모형이 설명할 수 있다는 것으로 요약된다. 이와 같은 내용을 기초로 회귀모형 적절성 평가에 대한 논의를 하고자 한다. 회귀 모형 분석의 목적은 조건부 확률변수y|x 의 미지의 누적확률분포를 추론하는 것이라고 할 수 있다. 본 논문에서는 누적확률분포 추론 과정에서 모형을 가정한 회귀함수와 분산함수의 평활 추정치를 모형을 가정하지 않은 회귀함수와 분산함수의 평활 추정치와 비교하고자 한다. 왜냐하면 회귀함수와 분산함수가 회귀 모형의 기본적인 속성을 포함하고 있기 때문이다.

Exploring central subspace via contour regression

이학배,Pilkeun Choi 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.1

Contour regression, a method for estimating the central subspace in regression, is based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the central subspace and can be extracted according to two measures of variation in the response: simple and general contour regression (SCR and GCR). When the elliptically contoured distribution and mild assumptions hold, the contour regression approach in comparison with existing sufficient dimension reduction methods suggests exhaustiveness of the central space, keeping √n-consistency. In addition, the contour-based approach proves robust to violations of departures from ellipticity. In this paper, two kernel simple and general contour regressions (KSCR and KGCR) are proposed and compared with SCR and GCR.

A note on statistical inference for differences of covariances

이학배 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.4

This article investigates statistical inferences about differences of covariances matrices when the response has more than two values. The subspace constructed by differences of covariance matrices is related to the sufficient dimension subspace and the central space. The asymptotic distribution of test statistic for structural dimension is outlined.

회귀그래픽 방법에서의 다중공선성

이학배(Hakbae Lee),최필근(Pilkeun Choi) 한국자료분석학회 2004 Journal of the Korean Data Analysis Society Vol.6 No.3

설명변수들의 다중공선성 문제는 회귀분석 실행 시 해결해야 할 문제 중의 하나이다. 다중공선성 문제는 모수들의 최소제곱 추정량을 추정하고 분석하는데 많은 어려움이 있다. 회귀그래픽방법은 다중공선성 문제를 선형성 조건으로 인식한다. 회귀그래픽 방법은 차원축소를 위해 설명변수들이 형성하는 중심부공간을 추정한다. 선형성 조건은 차원축소를 이루기 위해 중심부공간을 인지하고 추정하는데 있어 매우 효율적인 조건이 된다. 전통적인 회귀분석 과정에서 해결해야 할 설명변수들의 다중공선성 문제를 회귀그래픽 방법은 설명변수들의 선형성 조건이라 정의하고 중심부공간 추정에 있어 선행조건으로 취하는 것이다. 본 논문은 이러한 설명변수들의 선형성 조건과 다중공선성의 연관성과 차이점 그리고 회귀 그래픽 방법을 적용하는데 있어 어떻게 응용되는지 논의한다. Multicollinearity of predictor variables is known as one of cumbersome problems in regression analysis. Multicollinearity makes us impossible to obtain least square estimates of parameters. The goal of regression graphical method is to estimate central subspace spanned by the predictor variables. Linearity condition is efficient for recognizing and estimating the central subspace. While traditional regression method overcome multicollinearity, regression graphical method refer to multicollinearity as linearity condition. This paper explores multicollinearity in regression graphical method, discusses association and difference between multicollinearity and linearity condition. In addition, we investigate applicability of linearity condition to regression graphical methid.

Comparative Analysis for Multiple Testing Procedures with Binary Data

곽민정,이학배,윤민 한국자료분석학회 2015 Journal of the Korean Data Analysis Society Vol.17 No.1

Multiplicity problems frequently arise in data analysis. We review the multiple testing procedures with binary data. Especially with binary data, discreteness and ignorance of correlation structures in adjustment of multiplicity result in the loss of power. We review single step tests and stepwise tests as multiple testing procedures. We discuss single step tests such as Bonferroni and Sidak procedures and more powerful stepwise closed testing procedures such as the Holm and Hochberg procedures. We also, provide an overview of the methods of resampling-based multiplicity adjustment introduced by Westfall, Young (1993) and discuss the subset pivotality condition in discrete distribution. Multiple testing procedures are compared through simulation study and familywise error rates of these methods are presented. The familywise error rates of all multiple testing procedures do not exceed the nominal level. Among multiple testing procedures, the resampling-based methods are less conservative than single step tests and stepwise tests.

수리계획법을 이용한 서포트 벡터 기계 방법에 관한 연구

윤민,이학배,Yoon, Min,Lee, Hak-Bae 한국통계학회 2005 응용통계연구 Vol.18 No.2

기계학습은 패턴분류의 한 도구로써 광범위하게 연구되고 있다. 기계학습 방법들 중에서 서포트 벡터 기계(Support Vector Machines)는 많은 분야에서 연구되어지는 것으로 이진 패턴 분류문제에서 고차원의 특징공간에서 두 집합들 사이에 가장 큰 분리를 제공하는 최대 여유도(margin)를 가지는 분리 초평면을 찾는 것이다. 최대 여유도의 분리의 개념에 기초하여 Mangasarian(1968)은 다중-표면 방법(multi-surface method)을 제안하였고, 1980년대에 목적 계획법을 이용한 방법들이 광범위하게 개발되었다. 본 논문에서는 다목적 계획법과 목적 계획법을 이용한 수리계획법인 서포트 벡터 기계의 두가지 방법들을 제안하고 수치 예제들을 통하여 효용성에 대하여 논의하고자 한다. Machine learning has been extensively studied in recent years as effective tools in pattern classification problem. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problem with two class sets, the idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. However, the idea of maximal margin separation is not quite new: in 1960's the multi-surface method (MSM) was suggested by Mangasarian. In 1980's, linear classifiers using goal programming were developed extensively. This paper proposes a new family of SVM using MOP/GP techniques, and discusses its effectiveness throughout several numerical experiments.

Dimension Reduction and Prediction for High-dimensional Regression Models Using the Graphical Lasso

오언정,이학배 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.5

Deriving reductions from high-dimensional covariates with minimal loss of information is an effective way of reducing covariate dimension and plays a pivotal role in sufficient dimension reduction (SDR). We investigate sufficient dimension reduction in high- dimensional regressions by using the graphical lasso method developed by Friedman, Hastie, Tibshirani (2007) even when the sample size n is not sufficiently large compared to the number of predictors p. The key point here is that we consider the model in abundant high- dimensional regressions where most of the covariates contribute some information on a response, which differ from sparse regressions. By discovering an intrinsic dimensionality of the data and estimating a sufficient reduction R(X), we improve the prediction of the response, which is our ultimate goal, with a kernel-type estimator. The estimated reductions and predicted values of the response are illustrated through simulation studies and a real data application.

An Empirical Study on Dimension Reduction

서창희,이학배 한국자료분석학회 2018 Journal of the Korean Data Analysis Society Vol.20 No.6

The two inverse regression estimation methods, SIR and SAVE to estimate the central space are computationally easy and are widely used. However, SIR and SAVE may have poor performance in finite samples and need strong assumptions (linearity and/or constant covariance conditions) on predictors. The two non-parametric estimation methods, MAVE and dMAVE have much better performance for finite samples than SIR and SAVE. MAVE and dMAVE need no strong requirements on predictors or on the response variable. MAVE is focused on estimating the central mean subspace, but dMAVE is to estimate the central space. This paper explores and compares four methods to explain the dimension reduction. Each algorithm of these four methods is reviewed. Empirical study for simulated data shows that MAVE and dMAVE has relatively better performance than SIR and SAVE, regardless of not only different models but also different distributional assumptions of predictors. However, real data example with the binary response demonstrates that SAVE is better than other methods.

Structural Relationships among Customer Loyalty, Satisfaction and Trust of Internet Banking

강왈구,이학배 한국자료분석학회 2012 Journal of the Korean Data Analysis Society Vol.14 No.3

This study is to suggest the direction of expanding the use of Saemaeul Geumgo internet banking service through a variables analysis affecting customer loyalty. Website quality has a positive impact on customer satisfaction and trust. Corporate image is positively correlated with customer satisfaction and customer trust. The social presence has a positive impact on customer satisfaction and loyalty. Customer trust is positively correlated with customer satisfaction and loyalty. Customer satisfaction has a positive impact on customer loyalty. In order to enlarge the usage of Saemaeul Geumgo internet banking, Saemaeul Geumgo must prepare various measures for enhancing customer loyalty by using this research result.