선형회귀에서 표준화 회귀계수에 대한 소고

강명욱 한국자료분석학회 2017 Journal of the Korean Data Analysis Society Vol.19 No.1

In most social science research work there are some interests concerning the rank of relative importance of different variables in the regression model. Statistical packages such as SPSS provide the printouts on the standardized coefficient. But many people make cautionary remarks that the rankings of the standardized coefficients in terms of absolute magnitude does not necessarily reflect the importance of variables in explaining the variability of response variable. Many textbooks give warnings against the misuse of this automatic computer generated output. We consider the relationship between this standardized coefficient and the correlation coefficients of various residual plots. And this suggests that the appropriate correlation coefficients may be used in ranking the relative importance of variables. The correlation coefficient derived from added variable plot is a good measure in determining the ranks of variables according to the size of partial t-values for regression coefficient. The correlation coefficient from the additional R^2 plot compares each variable's contribution in terms of additional increase of coefficient of determination over the variability explained by other variables in the model. 대부분의 사회과학분야 연구에서는 다중선형회귀모형에 포함되는 설명변수들의 상대적 중요도에 대해 많은 관심을 가지고 있다. SPSS를 비롯한 여러 상용 통계패키지에서는 표준화 회귀계수의 추정값을 계산해 주고 있으며 표준화 회귀계수의 추정값의 절대값이 큰 설명변수가 중요하다고 해석하기도 하지만 이러한 주장에는 많은 논란이 있다. 여러 회귀분석 교과서에서도 표준화 회귀계수의 맹목적인 사용에 유의할 필요가 있다고 강조하고 있지만 대안은 제시되고 있지 않다. 본 연구에서는 설명변수의 상대적 중요도에 대한 구체적인 의미를 생각해보고 몇 가지 잔차산점도에서의 상관계수와 표준화 회귀계수의 관계를 알아보고 설명변수들의 상대적 중요도를 나타내는 적절한 척도를 제안한다. 추가변수그림의 상관계수는 추가적인 설명력을 검정하는 부분 검정통계량의 크기를 나타내는 척도로 사용될 수 있고, 추가결정계수그림의 상관계수는 설명변수의 추가를 통해서 발생하는 결정계수의 증가분을 나타내는 척도로 사용될 수 있다. 또한 보정계수를 이용하여 이러한 척도들과 표준화 회귀계수와의 관계를 구해본다. 제시된 척도들을 실제 자료에 적용시켜본다.

다중회귀분석에서 설명변수의 상대적 중요도 지표에 관한 연구

모유선,한상태,연규필,강현철 한국자료분석학회 2015 Journal of the Korean Data Analysis Society Vol.17 No.6

One of the important objectives in multiple regression analysis is to study on the variable importance in the model. Commonly used measures such as zero order correlation coefficients or standardized regression coefficients are not suitable for the purpose of verifying the relative importance of explanatory variables in the regression model. Therefore, several indicators have been proposed in order to measure the magnitude of importance of each explanatory variable and determine their rank orders. Especially, these indicators are mostly devised to treat the variable importance appropriately when there exists multicollinearity among independent variables in a regression model. In this article, we aim to investigate the characteristics and limitation of various measures for variable importance such as product measure, general dominance index, and relative weight in a multiple regression model. We expect that researchers using regression analysis can have more valuable interpretation for the constructed model by using these importance measures together with the conventional tools such as simple correlations, standardized regression coefficients. 다중회귀분석은 관심의 대상인 반응변수가 여러 개의 설명변수에 의해서 어떻게 설명되고 예측되는가에 대하여 다양한 분야에서 사용되고 있는 분석 기법 중 하나이다. 각각의 설명변수들에 대하여 중요도를 할당하는 것은 분석 결과의 정확한 해석을 위한 회귀분석의 주요한 연구 목표 중 하나로서, 기존의 여러 연구들을 통해 설명변수의 상대적 중요도를 결정할 수 있는 여러 지표들이 제안되었다. 특히, 이러한 지표들은 주로 변수들 간의 다중공선성이 있는 경우에 각 변수의 중요도를 적절히 측정할 수 있도록 고안되었다. 본 논문에서는 회귀분석에서 설명변수에 대한 해석을 위해 주로 사용되는 측도인 표준화 회귀계수, 상관계수 등이 변수의 중요도 지표로서 갖는 한계를 살펴보고, 대안적으로 제안된 곱측도(product measure), 일반우세지수(general dominance index), 상대가중치(relative weights) 등의 중요도 지표들의 특성과 차이점을 요약 정리함으로써 각 지표의 올바른 활용방안을 제시하고자 한다.

Deep Varying Coefficient Censored Regression Model

심주용,손인석,황창하,박혜정,이형록,석경하 계명대학교 자연과학연구소 2023 Quantitative Bio-Science Vol.42 No.2

In this study, we introduce deepVCCR, a deep learning-based method for varying coefficient censored regression. DeepVCCR harnesses the power of deep learning by combining the fundamental principles of censored regression and varying coefficient regression models. Both censored regression and varying coefficient regression models are widely used statistical techniques with diverse applications. However, we propose leveraging deep learning techniques to address the challenges inherent in high-dimensional and complex data analysis. Our experiments confirm the effectiveness of deepVCCR in managing such data and delivering superior performance compared to existing methods.

Quantile regression for robust inference on varying coefficient partially nonlinear models

Jing Yang,Fang Lu,Hu Yang 한국통계학회 2018 Journal of the Korean Statistical Society Vol.47 No.2

In this paper, we propose a robust statistical inference approach for the varying coefficient partially nonlinear models based on quantile regression. A three-stage estimation procedure is developed to estimate the parameter and coefficient functions involved in the model. Under some mild regularity conditions, the asymptotic properties of the resulted estimators are established. Some simulation studies are conducted to evaluate the finite performance as well as the robustness of our proposed quantile regression method versus the well known profile least squares estimation procedure. Moreover, the Boston housing price data is given to further illustrate the application of the new method.

The Time-Varying Coefficient Fama - French Five Factor Model: A Case Study in the Return of Japan Portfolios

LIAMMUKDA, Asama,KHAMKONG, Manad,SAENCHAN, Lampang,HONGSAKULVASU, Napon Korea Distribution Science Association 2020 The Journal of Asian Finance, Economics and Busine Vol.7 No.10

In this paper, we have developed a Fama - French five factor model (FF5 model) from Fama & French (2015) by using concept of time-varying coefficient. For a data set, we have used monthly data form Kenneth R. French home page, it include Japan portfolios (classified by using size and book-to-market) and 5 factors from July 1990 to April 2020. The first analysis, we used Augmented Dickey-Fuller test (ADF test) for the stationary test, from the result, all Japan portfolios and 5 factors are stationary. Next analysis, we estimated a coefficient of Fama - French five factor model by using a generalized additive model with a thin-plate spline to create the time-varying coefficient Fama - French five factor model (TV-FF5 model). The benefit of this study is TV-FF5 model which can capture a different effect at different times of 5 factors but the traditional FF5 model can't do it. From the result, we can show a time-varying coefficient in all factors and in all portfolios, for time-varying coefficients of Rm-Rf, SMB, and HML are significant for all Japan portfolios, time-varying coefficients of RMW are positively significant for SM, and SH portfolio and time-varying coefficients of CMA are significant for SM, SH, and BM portfolio.

Robust estimation and variable selection for varying-coefficient partially nonlinear models based on modal regression

Xiao Yanting,Liang Lulu 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.3

In this paper, we propose a robust two-stage estimation and variable selection procedure for varying-coefficient partially nonlinear model based on modal regression. In the first stage, each coefficient function is approximated by B-spline basis functions and then QR decomposition is employed to remove the nonparametric component from the original model. For the simple parametric model, an estimation and variable selection procedure for parameter is proposed based on modal regression. In the second stage, similar procedure for coefficient function is developed. The proposed procedure is not only flexible and easy to implement, but also is robust and efficient. Under some mild conditions, certain asymptotic properties of the resulting estimators are established. Moreover, the bandwidth selection and estimation algorithm for the proposed method is discussed. Furthermore, we conduct some simulations and a real example to evaluate the performances of the proposed estimation and variable selection procedure in finite samples.

Estimating Hydrodynamic Coefficients of Real Ships Using AIS Data and Support Vector Regression

VU HOANG THIEN,박종열,윤현규 한국해양공학회 2023 韓國海洋工學會誌 Vol.37 No.5

In response to the complexity and time demands of conventional methods for estimating the hydrodynamic coefficients, this study aims to revolutionize ship maneuvering analysis by utilizing automatic identification system (AIS) data and the Support Vector Regression (SVR) algorithm. The AIS data were collected and processed to remove outliers and impute missing values. The rate of turn (ROT), speed over ground (SOG), course over ground (COG) and heading (HDG) in AIS data were used to calculate the rudder angle and ship velocity components, which were then used as training data for a regression model. The accuracy and efficiency of the algorithm were validated by comparing SVR-based estimated hydrodynamic coefficients and the original hydrodynamic coefficients of the Mariner class vessel. The validated SVR algorithm was then applied to estimate the hydrodynamic coefficients for real ships using AIS data. The turning circle test was simulated from calculated hydrodynamic coefficients and compared with the AIS data. The research results demonstrate the effectiveness of the SVR model in accurately estimating the hydrodynamic coefficients from the AIS data. In conclusion, this study proposes the viability of employing SVR model and AIS data for accurately estimating the hydrodynamic coefficients. It offers a practical approach to ship maneuvering prediction and control in the maritime industry.

Computation of Design Coefficients in Ogee-crested Spillway Structure Using GEP and Regression Models

T. Bagatur,F. Onen 대한토목학회 2016 KSCE JOURNAL OF CIVIL ENGINEERING Vol.20 No.2

The ogee-crested spillway is a passage in a dam through which the design flood could be disposed of safely to the downstream. Spillways of improper design or insufficient capacities have caused failures of dams. Therefore, the spillway must be hydraulically and structurally adequate. This paper presents Gene-Expression Programming (GEP) models as an alternative approach to prediction of design coefficients in ogee-crested spillway structure. New formulations for prediction of design coefficient are developed using GEP and regression models. The performance of GEP was found to be satisfactory and encouraging when compared with regression model in predicting of design coefficient. This capability of GEP makes it unique and more effective when compared with regression models evaluated in this paper. The superior performance of GEP is attributed to the powerful Artificial Intelligence (AI) techniques for computer learning inspired by natural evolution to find the appropriate mathematical model (expression) to fit a set of fits. This study highlights the utility of AI-based models with a view to increase their usage by engineers and planners working on spillway design problems.

Predicting the resting metabolic rate of young and middle-aged healthy Korean adults: A preliminary study

( Hun-young Park ),( Won-sang Jung ),( Hyejung Hwang ),( Sung-woo Kim ),( Jisu Kim ),( Kiwon Lim ) 한국운동영양학회 2020 Physical Activity and Nutrition (Phys Act Nutr) Vol.24 No.1

[Purpose] This preliminary study aimed to develop a regression model to estimate the resting metabolic rate (RMR) of young and middle-aged Koreans using various easy-to-measure dependent variables. [Methods] The RMR and the dependent variables for its estimation (e.g. age, height, body mass index, fat-free mass; FFM, fat mass, % body fat, systolic blood pressure, diastolic blood pressure, mean arterial pressure, pulse pressure, and resting heart rate) were measured in 53 young (male n = 18, female n = 16) and middle-aged (male n = 5, female n = 14) healthy adults. Statistical analysis was performed to develop an RMR estimation regression model using the stepwise regression method. [Results] We confirmed that FFM and age were important variables in both the regression models based on the regression coefficients. Mean explanatory power of RMR1 regression models estimated only by FFM was 66.7% (R²) and 66.0% (adjusted R²), while mean standard errors of estimates (SEE) was 219.85 kcal/ day. Additionally, mean explanatory power of RMR2 regression models developed by FFM and age were 70.0% (R²) and 68.8% (adjusted R²), while the mean SEE was 210.64 kcal/day. There was no significant difference between the measured RMR by the canopy method using a metabolic gas analyzer and the predicted RMR by RMR1 and RMR2 equations. [Conclusion] This preliminary study developed a regression model to estimate the RMR of young and middle-age healthy Koreans. The regression model was as follows: RMR1 = 24.383 × FFM + 634.310, RMR2 = 23.691 × FFM - 5.745 × age + 852.341.

다변량 선형회귀분석을 이용한 증발접시계수 산정방법 적용성 검토

임창수 한국수자원학회 2022 한국수자원학회논문집 Vol.55 No.3

The effects of monthly meteorological data measured at 11 stations in South Korea on pan coefficient were analyzed to develop the four types of multiple linear regression models for estimating pan coefficients. To evaluate the applicability of developed models, the models were compared with six previous models. Pan coefficients were most affected by air temperature for January, February, March, July, November and December, and by solar radiation for other months. On the whole, for 12 months of the year, the effects of wind speed and relative humidity on pan coefficient were less significant, compared with those of air temperature and solar radiation. For all meteorological stations and months, the model developed by applying 5 independent variables (wind speed, relative humidity, air temperature, ratio of sunshine duration and daylight duration, and solar radiation) for each station was the most effective for evaporation estimation. The model validation results indicate that the multiple linear regression models can be applied to some particular stations and months. 우리나라 11개 기상관측지역의 월별 기상자료가 증발접시계수에 미치는 영향을 분석하고, 증발접시계수 산정을 위한 4가지 형태의 다변량 선형회귀모형의 적용성을 검토하였다. 개발된 증발접시계수 산정모형의 적용성을 평가하기 위해서 기존에 다른 연구자들에 의해서 제안된 6가지의 모형과 비교 평가하였다. 우리나라 11개 기상관측지역에서 증발접시계수는 1, 2, 3, 7, 11, 12월은 기온에 가장 큰 영향을 받고, 다른 월들은 일사량에 가장 큰 영향을 받는 것으로 나타났다. 전반적으로 모든 월에서 풍속과 상대습도는 기온이나 일사량과 비교해서 증발접시계수에 큰 영향을 미치지 않는 것으로 나타났다. 모든 지역과 월에서 각 지역별로 5개의 독립변수(풍속, 상대습도, 기온, 일조시간과 가조시간의 비, 일사량)를 적용하여 유도된 모형이 가장 양호한 증발량 산정 결과를 보였다. 모형 검증결과에 의하면 다변량 선형회귀분석을 적용하여 증발접시계수를 산정하는 경우 일부 지역과 월에서 제한적으로 적용할 수 있을 것으로 판단된다.