MULTIPLE OUTLIER DETECTION IN LOGISTIC REGRESSION BY USING INFLUENCE MATRIX

Lee, Gwi-Hyun,Park, Sung-Hyun The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.4

Many procedures are available to identify a single outlier or an isolated influential point in linear regression and logistic regression. But the detection of influential points or multiple outliers is more difficult, owing to masking and swamping problems. The multiple outlier detection methods for logistic regression have not been studied from the points of direct procedure yet. In this paper we consider the direct methods for logistic regression by extending the $Pe\tilde{n}a$ and Yohai (1995) influence matrix algorithm. We define the influence matrix in logistic regression by using Cook's distance in logistic regression, and test multiple outliers by using the mean shift model. To show accuracy of the proposed multiple outlier detection algorithm, we simulate artificial data including multiple outliers with masking and swamping.

Multiple deletion measures of test statistics inmultivariate regression

Kang-Mo Jung 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4

In multivariate regression analysis there exist many influence measures on the regression estimates. However it seems to be few of influence diagnostics on test statistics in hypothesis testing. Case-deletion approach is fundamental for investigating influence of observations on estimates or statistics. Tang and Fung (1997) derived single case-deletion of the Wilks’ ratio, Lawley-Hotelling trace, Pillai’s trace for testing a general linear hypothesis of the regression coefficients in multivariate regression. In this paper we derived more extended form of those measures to deal with joint influence among observations. A numerical example is given to illustrate the effect of joint influence on the test statistics. In multivariate regression analysis there exist many influence measures on the regression estimates. However it seems to be few of influence diagnostics on test statistics in hypothesis testing. Case-deletion approach is fundamental for investigating influence of observations on estimates or statistics. Tang and Fung (1997) derived single case-deletion of the Wilks’ ratio, Lawley-Hotelling trace, Pillai’s trace for testing a general linear hypothesis of the regression coefficients in multivariate regression. In this paper we derived more extended form of those measures to deal with joint influence among observations. A numerical example is given to illustrate the effect of joint influence on the test statistics.

Multiple Outlier Detection in Logistic Regression by using Influence Matrix

Gwi Hyun Lee,박성현 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.4

Many procedures are available to identify a single outlier or an isolatedinuential point in linear regression and logistic regression. But the detectionof inuential points or multiple outliers is more dicult, owing to maskingand swamping problems. The multiple outlier detection methods for logisticregression have not been studied from the points of direct procedure yet. Inthis paper we consider the direct methods for logistic regression by extend-ing the Pe~na and Yohai (1995) inuence matrix algorithm. We dene theinuence matrix in logistic regression by using Cook's distance in logistic re-gression, and test multiple outliers by using the mean shift model. To showaccuracy of the proposed multiple outlier detection algorithm, we simulatearticial data including multiple outliers with masking and swamping.

Comparison of Two Numerical Models on Photosynthetic Response of Quercus mongolica Leaves to Air Pollutants

Kim, Joon Ho,Ihm, Byung Sun,Kim, Jong Wook 한국식물학회 1999 Journal of Plant Biology Vol.42 No.1

A multiple-regression model is presented for estimating the effect of major air pollutants on net photosynthetic rate (Pn) of Quercus mongolica leaves, of which visible injury is not shown. Photosynthetic capacity was found to be primarily a function of PPFD, air temperature (T) and ambient ozone (O_3) concentration. The negative direction of photosynthetic capacity response to O_3 concentration indicates a potential growth reduction of Q. mongolica due to ambient O_3 concentration in the urban areas of Korea. The model was compared with a non-linear regression model including the same variables. We assessed the contribution of variables to two two models of ambient O_3 affecting Pn of Q. mongolica leaves. The mean Pn difference between the models with and without ambient O_3 in the multiple-regression was smaller than that in the non-linear regression. The relative contributions of ambient O_3 to multiple-regression and non-linear regression were 12.6% and 5.6%, respectively. The results indicate that multiple-regression models can be applicable for qualitative or quantitative assessment of the effect of air pollutants on Pn response of plant leaves, of which visible injury may not be shown in situ. Also, the assessment of ecophysiological effects using numerical models will have a degree of uncertainty associated with the measuring time/period of the field data used in the modelling, as well as the numerical structure of the models.

다중회귀모형을 이용한 수완부 골성숙도의 추정에 관한 연구

김경호,유형석,김석현 대한치과교정학회 1997 대한치과교정학회지 Vol.27 No.5

성장의 잠재력에 대한 평가는 개체의 성숙도를 나타내는 여러 생리학적 지표(physiologic indicators)들에 의해 이루어지며 그 중 골성숙도(skeletal maturity)는 성적성숙도(sexual maturity)와 신장의 성장변화와 밀접한 관계가 있는 것으로 알려져 있으나, 치아발육과의 상관관계에 대해선 논란이 많은 실정이다. 그러나 최근의 연구에 의하면 하악견치를 포함한 일부치아의 발육이 골성숙도와 밀접한 관련이 있는 것으로 알려져 있으나, 치아발육과의 상관관계에 대해선 논란이 많은 실정이다. 그러나 최근의 연구에 의하면 하악 견치를 포함한 일부 치아의 발육이 골성숙도와 밀접한 관련이 있는 것으로 보고된 바 있다. 이에, 본 연구에서는 7세에서 15세까지의 한국인 남, 녀 아동 387명의 수완부 방사선 사진과 파노라마 사진을 이용하여 Fishman방법과 Greulich와 Pyle방법에 의해 골성숙도을 평가하였으며 변형된 Demirjiran방법에 의해 치아의 성숙도를 평가하여, 수완부 방사선의 사진의 도움 없이 골성숙도를 추정할수 있는 방법을 구하고자 다중회귀모형을 이용한 수완부 골성숙도의 추정에 관한 연구를 시행하였으며 다음과 같은 결론을 얻었다. 1. 골성숙 지수의 추정을 위한 아래의 다중회귀모형은 84%의 설명력을 나타내며 연대연령, 성별, 하악 견치의 회귀계수는 통계학적 유의성을 보였다. 골성숙지수 = 0.60x 연대연령 -1.67x성별 + 0.88x하악견치 - 0.05x하악 제2대구치 -10.3 2. 골연령의 추정을 위한 아래의 다중회귀모형은 87%의 설명력을 나타내며 연대연령, 성별, 하악 견치의 회귀계수는 통계학적 유의성을 보였다. 골연령 = 0.75x 연대연령 - 0.55x성별 + 0.71x하악 견치 + 0.09x하악 제2대구치- 5.77 (성별: 남자=1, 여자=0., 하악견치, 제2대구치 : 각 발육단계별 평균연령) The evaluation of growth potency can be done with many physiologic indicators. It has been well known that skeletal maturity has a close relation with both sexual maturity somatic maturity, but the correlation between skeletal maturity and dental maturity was believed to be less certain. But, recent studies show that specific teeth, including lower canines, present close correlations with skeletal maturity. So, in this study, we study, we studied hand-wrist X-ray films and orthopantomograms of 387 Korean boys and girls aged from 7 to 15; the purpose was to determine skeletal and dental maturity, and to find out a new method to estimate individual skeletal maturity using multiple-regression model, without the help of hand-wrist X-ray film. As a result of this study, followings were observed. 1. The following multiple-regression model can estimate skeletal maturity index(SMI) with 84% of accuracy, and regression coefficient of chronologic age, sex and lower canine show statistical significance. SMI = 0.60 x chronologic age - 1.67 x sex** + 0.88 x lower canine* - 0.05 x lower 2nd molar* - 10.3 *: mean age corresponding each developing atage, **: male= 1, femal = 0 2. The following multiple-regression model can estimate skeletal age with 87% of accuracy, and regression coefficient of chronologic age, sex and lower canine show statistical significance. Skeletal age = 0.75 x chronologic age - 0.55 x sex** + 0.71 x lower canine* - 0.09 x lower 2nd molar* - 5.77 *: mean age corresponding each developing atage, **: male= 1, femal = 0

경제지표를 활용한 다중선형회귀 모델 기반 국제 휘발유 가격 예측

한명은,김지연,이현희,김세인,박민서 국제문화기술진흥원 2024 The Journal of the Convergence on Culture Technolo Vol.10 No.1

The domestic petroleum market is highly sensitive to changes in international oil prices. So, it is important to identify and respond to those changes. In particular, it is necessary to clearly understand the factors causing the price fluctuations of gasoline, which exhibits high consumption. International gasoline prices are influenced by global factors such as gasoline supplies, geopolitical events, and fluctuations in the U.S. dollar. However, previous studies have only focused on gasoline supplies. In this study, we explore the causal relationship between economic indicators and international gasoline prices using various machine learning-based regression models. First, we collect data on various global economic indicators. Second, we perform data preprocessing. Third, we model using Multiple linear regression, Ridge regression, and Lasso(Least Absolute Shrinkage and Selection Operator) regression. The multiple linear regression model showed the highest accuracy at 96.73% in test sets. As a result, Our Multiple linear regression model showed the highest accuracy at 96.73% in test sets. We will expect that our proposed model will be helpful for domestic economic stability and energy policy decisions.

다중선형회귀법을 활용한 예민화와 환경변수에 따른 AL-6XN강의 공식특성 예측

정광후 ( Kwang-hu Jung ),김성종 ( Seong-jong Kim ) 한국부식방식학회 2020 Corrosion Science and Technology Vol.19 No.6

This study aimed to predict the pitting corrosion characteristics of AL-6XN super-austenitic steel using multiple linear regression. The variables used in the model are degree of sensitization, temperature, and pH. Experiments were designed and cyclic polarization curve tests were conducted accordingly. The data obtained from the cyclic polarization curve tests were used as training data for the multiple linear regression model. The significance of each factor in the response (critical pitting potential, repassivation potential) was analyzed. The multiple linear regression model was validated using experimental conditions that were not included in the training data. As a result, the degree of sensitization showed a greater effect than the other variables. Multiple linear regression showed poor performance for prediction of repassivation potential. On the other hand, the model showed a considerable degree of predictive performance for critical pitting potential. The coefficient of determination (R²) was 0.7745. The possibility for pitting potential prediction was confirmed using multiple linear regression.

다중선형회귀모델 기반 고출력 직렬 배터리 팩의 전압불균형 추정

김승우,이평연,한동호,김종훈 한국전기전자학회 2019 전기전자학회논문지 Vol.23 No.1

In this paper, the electrical characteristics with various C-rates are tested with a high power series battery packcomprised of 18650 cylindrical nickel cobalt aluminum(NCA) lithium-ion battery. The electrical characteristics ofdischarge capacity test with 14S1P battery pack and electric vehicle (EV) cycle test with 4S1P battery pack arecompared and analyzed by the various of C-rates. Multiple linear regression is used to estimate voltage imbalance of14S1P and 4S1P battery packs with various C-rates based on experimental data. The estimation accuracy is evaluatedby root mean square error(RMSE) to validate multiple linear regression. The result of this paper is contributed that touse for estimating the voltage imbalance of discharge capacity test with 14S1P battery pack using multiple linearregression better than to use the voltage imbalance of EV cycle with 4S1P battery pack 본 논문에서는 18650 원통형 NCA 리튬이온 배터리로 구성된 고출력 직렬 배터리로 다양한 C-rate의 전기적 특성을 테스트한다. 테스트를 통해 추출한 14S1P 배터리 팩의 방전 용량 데이터와 4S1P 배터리 팩의 EV cycle 데이터를 통해 C-rate의변화에 따른 전기적 특성을 분석한다. 분석을 통해 얻은 데이터를 기반으로 C-rate에 따른 방전용량 실험의 셀 간 전압 편차와 EV cycle 실험의 셀 간 전압 편차를 다중선형회귀 모델로 추정하여 선형적인 특징을 가진 데이터와 비선형적인 특징을가진 데이터에 대한 각각의 추정성능을 검증한다. 모델의 추정성능을 검증하기 위해 추정 데이터와 실제 데이터의 RMSE를구해 알고리즘의 정확성을 평가한다. 논문의 결과는 14S1P 배터리 팩의 방전 용량의 셀 간 전압 불균형과 4S1P 배터리 팩의EV cycle의 셀 간 전압 불균형 중 선형적인 데이터인 방전 용량의 셀 간 불균형 데이터의 추정 성능이 더 뛰어난 것을 검증하는데 기여한다.

회귀분석법을 이용한 차량 오일펌프의 인로터 중량 최적화 해석

정대근(Dae-geun Jung),김기태(Ki-Tae Kim) 한국자동차공학회 2020 한국자동차공학회 학술대회 및 전시회 Vol.2020 No.11

This white paper contains information on techniques that can reduce design time. In this study, multiple regression analysis was used as a method to increase work efficiency. The vane, in-rotor of the vehicle oil pump was selected. Variables that can be optimized for weight were selected during design. It has 5 independent variables and 3 factors, which was analyzed by multiple regression. Based on this data, the “Macro” automation sheet was built. As a result of comparing the opimization program and CAE in this paper, the reliability was 91.6%. Through this, the designer can easily and quickly predict design variables without CAE analysis.

한계와 이상치가 있는 결측치의 로버스트 다중대체 방법

박유성,오도영,권태연 한국통계학회 2019 응용통계연구 Vol.32 No.6

The problem of missing value imputation for variables in surveys that include item missing becomes complicated if outliers and logical boundary conditions between other survey items cannot be ignored. If there are outliers and boundaries in a variable including missing values, imputed values based on previous regression-based imputation methods are likely to be biased and not meet boundary conditions. In this paper, we approach these difficulties in imputation by combining various robust regression models and multiple imputation methods. Through a simulation study on various scenarios of outliers and boundaries, we find and discuss the optimal combination of robust regression and multiple imputation method. 항목 무응답(item missing)이 발생한 설문조사에서 결측이 포함된 변수에 이상치(outlier)의 존재와 다른 설문문항 항목과의 논리적 한계(boundary) 조건들이 유의미하다면 결측치 대체문제는 매우 복잡해진다. 한계가 있는 결측값들을 포함한 변수에 이상치가 존재하는 경우, 기존의 회귀분석에 근거한 결측치 대체방법은 편향된 대체값 그리고 한계를 만족하지 않은 대체값을 제시할 가능성이 있다. 이에 본 논문은 회귀모형에 기반을 두고 결측치들을 대체를 함에 있어 이상치와 논리적 한계조건이 자료에 존재하는 경우, 다양한 로버스트 회귀모형과 다중대체 방법의 조합을 통해 해결점을 모색하고자 한다. 이를 위해 이들 방법들의 최적의 조합을 다양한 시나리오별로 모의실험을 통하여 찾아보고 이에 대하여 논의하였다.