• Title, Summary, Keyword: 다중공선성

### Procedure for the Selection of Principal Components in Principal Components Regression (주성분회귀분석에서 주성분선정을 위한 새로운 방법)

• Kim, Bu-Yong;Shin, Myung-Hee
• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.967-975
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• 2010
• Since the least squares estimation is not appropriate when multicollinearity exists among the regressors of the linear regression model, the principal components regression is used to deal with the multicollinearity problem. This article suggests a new procedure for the selection of suitable principal components. The procedure is based on the condition index instead of the eigenvalue. The principal components corresponding to the indices are removed from the model if any condition indices are larger than the upper limit of the cutoff value. On the other hand, the corresponding principal components are included if any condition indices are smaller than the lower limit. The forward inclusion method is employed to select proper principal components if any condition indices are between the upper limit and the lower limit. The limits are obtained from the linear model which is constructed on the basis of the conjoint analysis. The procedure is evaluated by Monte Carlo simulation in terms of the mean square error of estimator. The simulation results indicate that the proposed procedure is superior to the existing methods.

### Estimation of S&T Knowledge Production Function Using Principal Component Regression Model (주성분 회귀모형을 이용한 과학기술 지식생산함수 추정)

• Park, Su-Dong;Sung, Oong-Hyun
• Journal of Korea Technology Innovation Society
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• v.13 no.2
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• pp.231-251
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• 2010
• The numbers of SCI paper or patent in science and technology are expected to be related with the number of researcher and knowledge stock (R&D stock, paper stock, patent stock). The results of the regression model showed that severe multicollinearity existed and errors were made in the estimation and testing of regression coefficients. To solve the problem of multicollinearity and estimate the effect of the independent variable properly, principal component regression model were applied for three cases with S&T knowledge production. The estimated principal component regression function was transformed into original independent variables to interpret properly its effect. The analysis indicated that the principal component regression model was useful to estimate the effect of the highly correlate production factors and showed that the number of researcher, R&D stock, paper or patent stock had all positive effect on the production of paper or patent.

### A Study on Technology Level Evaluation based on Patent without Multicollinearity (특허기반의 기술수준평가 모형의 다중 공선성을 제거한 기술수준 평가모형 제안)

• Cho, Il-Gu;Oh, Jong-Hak
• Proceedings of the Korea Contents Association Conference
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• pp.461-462
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• 2014
• 기존 전문가 델파이 평가를 대체하는 특허기반 기술수준 평가모형들의 독립변수로 활용되는 특허활동도, 특허집중도, 특허시장력, 특허경쟁력 및 특허영향력의 다중공선성이 존재하여 이를 제거함으로써 보다 신뢰성이 높은 기술수준 평가모형을 실증하여 제안하고자 한다.

### Effects of Multicollinearity in Logit Model (로짓모형에 있어서 다중공선성의 영향에 관한 연구)

• Ryu, Si-Kyun
• Journal of Korean Society of Transportation
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• v.26 no.1
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• pp.113-126
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• 2008
• This research aims to explore the effects of multicollinearity on the reliability and goodness of fit of logit model. To investigate the effects of multicollinearity on the multinominal logit model, numerical experiments are performed. The exploratory variables(attributes of utility functions) which have a certain degree of correlations from (rho=) 0.0 to (rho=) 0.9 are generated and rho-squares and t-statistics which are the indices of goodness of fit and reliability of logit model are traced. From the well designed numerical experiments, following findings are validated : 1) When a new exploratory variable is added, some of rho-squares increase while the others decrease. 2) The higher relations between generic variables lead a logit model worse with respect to goodness of fit. 3) Multicollinearity has a tendency to produce over-evaluated parameters. 4) The reliability of the estimated parameter has a tendency to decrease when the correlations between attributes are high. These results suggest that we have to examine the existence of multicollinearity and perform the proper treatments to diminish multicollinearity when we develop logit model.

### Principal Components Regression in Logistic Model (로지스틱모형에서의 주성분회귀)

• Kim, Bu-Yong;Kahng, Myung-Wook
• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.571-580
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• 2008
• The logistic regression analysis is widely used in the area of customer relationship management and credit risk management. It is well known that the maximum likelihood estimation is not appropriate when multicollinearity exists among the regressors. Thus we propose the logistic principal components regression to deal with the multicollinearity problem. In particular, new method is suggested to select proper principal components. The selection method is based on the condition index instead of the eigenvalue. When a condition index is larger than the upper limit of cutoff value, principal component corresponding to the index is removed from the estimation. And hypothesis test is sequentially employed to eliminate the principal component when a condition index is between the upper limit and the lower limit. The limits are obtained by a linear model which is constructed on the basis of the conjoint analysis. The proposed method is evaluated by means of the variance of the estimates and the correct classification rate. The results indicate that the proposed method is superior to the existing method in terms of efficiency and goodness of fit.

### Development of model for prediction of land sliding at steep slopes (급경사지 붕괴 예측을 위한 모형 개발)

• Park, Ki-Byung;Joo, Yong-Sung;Park, Dug-Keun
• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.691-699
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• 2011
• Land sliding is one of well-known nature disaster. As a part of effort to reduce damage from land sliding, many researchers worked on increasing prediction ability. However, because previous studies are conducted mostly by non-statisticians, previously proposed models were hardly statistically justifiable. In this paper, we predicted the probability of land sliding using the logistic regression model. Since most explanatory variables under consideration were correlated, we proposed the final model after backward elimination process.

### Completion of the Missing Rainfall Data by a Multi-regression method (다중회귀분석을 이용한 강우량 결측치 보정)

• Lee, Myoung-Woo;Lee, Bong-Hee;Kim, Hung-Soo;Shim, Myung-Pil
• Proceedings of the Korea Water Resources Association Conference
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• pp.775-779
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• 2006
• 강우자료의 구축은 수문해석에 있어 가장 기본적이며 중요한 단계라 할 수 있다. 하지만 수문 관측 자료의 경우 결측치가 존재하여 그에 대한 보정이 필요한 경우가 종종 발생하게 된다. 따라서 수문자료의 분석을 수행하기에 앞서 우선 자료에 대한 검정을 실시하고, 결측치가 존재할 경우는 이를 보정하여 분석을 수행하여야 한다. 본 연구에서는 다변량통계기법의 하나인 다중회귀분석을 이용하여 강우 결측치를 보정하였다. 본 연구에서는 다중공선성과 자기상관에 대하여 고려한 다중회귀모형을 구성하였다. 모형의 구성시 모든 결측지점에 적용이 가능하지 않아 일반성이 떨어짐을 확인 할 수 있었지만, 모형이 구성될 경우 통계적 적합도와 유의수준을 확인 할 수 있는 장점이 있었으며, 다중회귀모형이 구성되는 경우 좋은 보정 결과를 주는 것을 확인 할 수 있었다.

### A Criterion for the Selection of Principal Components in the Robust Principal Component Regression (로버스트주성분회귀에서 최적의 주성분선정을 위한 기준)

• Kim, Bu-Yong
• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011
• Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.

### A Study on the Modal Split Model Using Zonal Data (존 데이터 기반 수단분담모형에 관한 연구)

• Ryu, Si-Kyun;Rho, Jeong-Hyun;Kim, Ji-Eun
• Journal of Korean Society of Transportation
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• v.30 no.1
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• pp.113-123
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• 2012
• This study introduces a new type of a modal split model that use zonal data instead of cost data as independent variables. It has been indicated that the ones using cost data have deficiencies in the multicollinearity of travel time and cost variables and unpredictability of independent variables. The zonal data employed in this study include (1) socioeconomic data, (2) land use data and (3) transportation system data. The test results showed that the proposed modal split model using zonal data performs better than the other does.

### Using Ridge Regression to Improve the Accuracy and Interpretation of the Hedonic Pricing Model : Focusing on apartments in Guro-gu, Seoul (능형회귀분석을 활용한 부동산 헤도닉 가격모형의 정확성 및 해석력 향상에 관한 연구 - 서울시 구로구 아파트를 대상으로 -)

• Koo, Bonsang;Shin, Byungjin
• Korean Journal of Construction Engineering and Management
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• v.16 no.5
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• pp.77-85
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• 2015
• The Hedonic Pricing model is the predominant approach used today to model the effect of relevant factors on real estate prices. These factors include intrinsic elements of a property such as floor areas, number of rooms, and parking spaces. Also, The model also accounts for the impact of amenities or undesirable facilities of a property's value. In the latter case, euclidean distances are typically used as the parameter to represent the proximity and its impact on prices. However, in situations where multiple facilities exist, multi-colinearity may exist between these parameters, which can result in multi-regression models with erroneous coefficients. This research uses Variance Inflation Factors(VIF) and Ridge Regression to identify these errors and thus create more accurate and stable models. The techniques were applied to apartments in Guro-gu of Seoul, whose prices are impacted by subway stations as well as a public prison, a railway terminal and a digital complex. The VIF identified colinearity between variables representing the terminal and the digital complex as well as the latitudinal coordinates. The ridge regression showed the need to remove two of these variables. The case study demonstrated that the application of these techniques were critical in developing accurate and robust Hedonic Pricing models.