Diagnostic In Spline Regression Model With Heteroscedasticity

Lee, In-Suk,Jung, Won-Tae,Jeong, Hye-Jeong Korean Data and Information Science Society 1995 한국데이터정보과학회지 Vol.6 No.1

We have consider the study of local influence for smoothing parameter estimates in spline regression model with heteroscedasticity. Practically, generalized cross-validation does not work well in the presence of heteroscedasticity. Thus we have proposed the local influence measure for generalized cross-validation estimates when errors are heteroscedastic. And we have examined effects of diagnostic by above measures through Hyperinflation data.

빅 데이터와 기계 학습의 시대 심리학 연구 모형의 평가 원칙과 방법

이태헌 한국심리학회 2021 한국심리학회지 일반 Vol.40 No.4

The objective of the present article is to explain principles of estimation and assessment for statistical models in psychological research. The principles have indeed been actively discussed over the past few decades in the field of mathematical and quantitative psychology. The essence of the discussion is as follows: 1) candidate models are to be considered not the true model but approximating models, 2) discrepancy between a candidate model and the true model will not disappear even in the population, and therefore 3) it would be best to select the approximating model exhibiting the smallest discrepancy with the true model. The discrepancy between the true model and a candidate model estimated in the sample has been referred to as overall discrepancy in quantitative psychology. In the field of machine learning, models are assessed in light of the extent to which performance of a model is generalizable to the new unseen samples, without being limited to the training samples. In machine learning, a model’s ability to generalize is referred to as the generalization error or prediction error. The present article elucidates the point that the principle of model assessment based on overall discrepancy advocated in quantitative psychology is identical to the model assessment principle based on generalization/prediction error firmly adopted in machine learning. Another objective of the present article is to help readers appreciate the fact that questionable data analytic practices widely tolerated in psychology, such as HARKing (Kerr, 1998) and QRP (Simmons et al., 2011), have been likely causes of the problem known as overfitting in individual studies, which in turn, have collectively resulted in the recent debates over replication crisis in psychology. As a remedy against the questionable practices, this article reintroduces cross-validation methods, whose initial discussion dates back at least to the 1950s in psychology (Mosier, 1951), by couching them in terms of estimators of the generalization/prediction error in the hope of reducing the overfitting problems in psychological research. 본 논문에서는 계량 심리학 분야에서 지난 수 십 년 동안 꾸준히 논의가 진행되어 왔던 모형 추정과 평가의 원칙을 심리학 연구자들에게 소개하는 것을 목적으로 한다. 계량 심리학 분야에서 진행된 논의의 핵심은 1) 후보 모형들은 참 모형(true model)이 아니라 근사 모형(approximating model)이며, 2) 데이터 크기가 무한히 커지더라도 참 모형과 근사 모형 간 불일치는 사라지는 것은 아니기 때문에, 3) 여러 후보 모형 중 참 모형과의 불일치가 가장 낮은 것으로 추정되는 근사 모형을 선정하는 것이 바람직하다는 것이다. 이러한 모형 선정의 원리는 4차 산업 혁명의 시대, 여러 학문 분야에 걸쳐 그 영역을 확장하고 있는 기계 학습(machine learning) 분야에서 채택하고 있는 모형 평가의 원칙과 동일함을 설명하였다. 즉, 기계 학습 분야에서는 훈련(training) 과정에 노출되지 않았던 새로운 사례에서 보이는 모형의 성능인 일반화 혹은 예측 오차(generalization or prediction error)를 추정함으로써 모형을 선정하는데, 이는 계량 심리학 분야에서 근사모형과 참모형의 불일치 추정량인 총체적 오차(overall discrepancy)를 추정함으로써 모형을 선정해야 한다는 원리와 동일함을 설명하였다. 본 논문의 두 번째 목적은, 이러한 모형 선정의 원칙에 대한 이해를 바탕으로, 현재 심리학 분야에서 주어진 데이터에 대한 “철저한” 분석 관행이 초래하는 과적합(overfitting) 문제와 그 해결 방안을 논의하는 데 있다. 특히, 기계 학습 분야에서 가정 널리 사용되고 있으며, 계량 심리학 분야에서도 오래전부터 논의가 되어온(Mosier, 1951) 교차-타당성 입증법(cross-validation)을 일반화 오차의 추정량이라는 관점에서 소개하고 사용을 당부하였다.

Public health relevance between air pollution and daily mortality rates

Minjae Park 한국신뢰성학회 2019 International Journal of Reliability and Applicati Vol.20 No.1

In this paper, we present generalized models to evaluate the daily mortality rates considering five major air pollutants affects including particulate matter <10 μm in aerodynamic diameter (PM10), carbon monoxide (CO), nitrogen dioxide (NO₂), sulfur dioxide (SO₂) and ozone (O₃) based on data from Seoul, South Korea (1999~2003) using generalized additive models. Stepwise function is used to find the best fit of generalized additive models. Despite much research on air pollutants with meteorological effects on daily death tolls, there has been little research assuming that air pollutants have non-linear relationships with daily death toll. To estimate the non-linear relationships between air pollutants and daily death tolls, we separate total data into training data and testing data and conduct cross validation. Using generalized additive models and generalized linear models, we determine the best fitting models with minimum Akaike Information Criterion. Seasonal factors are also considered. By sensitivity analysis, we investigate and measure how each air pollutant affects daily mortality rates. In all seasons, CO and SO₂ have nonlinear associations with daily death tolls. PM10 (RR=1.0027 for IQR 41.54 μg / m³ increment) doesn’t have a strong association with mortality rates and NO₂ (RR=1.0108 for IQR 17.29 increment) is only weakly associated with mortality.

Semiparametric least squares support vector machine for accelerated failure time model

심주용,김충락,황창하 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1

A lot of effort has been devoted to develop effective estimation methods for the accelerated failure time (AFT) model with censored data. The AFT model assumes a linear relationship between the logarithm of event time and covariates. In this paper we propose a semiparametric least squares support vector machine (LS-SVM) to consider situations where the functional form of the effect of one or more covariates is unknown. The proposed estimating equation can be easily computed by a simple linear equation system. We study the effect of several covariates on a censored response variable with an unknown probability distribution.Wealso provide a generalized cross-validation (GCV) method for choosing the hyperparameters which affect the performance of the proposed approach. The proposed method is evaluated through simulations and demonstrated using two real data examples.

Partially linear support vector orthogonal quantile regression with measurement errors

Hwang, Changha The Korean Data and Information Science Society 2015 한국데이터정보과학회지 Vol.26 No.1

Quantile regression models with covariate measurement errors have received a great deal of attention in both the theoretical and the applied statistical literature. A lot of effort has been devoted to develop effective estimation methods for such quantile regression models. In this paper we propose the partially linear support vector orthogonal quantile regression model in the presence of covariate measurement errors. We also provide a generalized approximate cross-validation method for choosing the hyperparameters and the ratios of the error variances which affect the performance of the proposed model. The proposed model is evaluated through simulations.

Semiparametric support vector machine for accelerated failure time model

Hwang, Chang-Ha,Shim, Joo-Yong The Korean Data and Information Science Society 2010 한국데이터정보과학회지 Vol.21 No.4

For the accelerated failure time (AFT) model a lot of effort has been devoted to develop effective estimation methods. AFT model assumes a linear relationship between the logarithm of event time and covariates. In this paper we propose a semiparametric support vector machine to consider situations where the functional form of the effect of one or more covariates is unknown. The proposed estimating equation can be computed by a quadratic programming and a linear equation. We study the effect of several covariates on a censored response variable with an unknown probability distribution. We also provide a generalized approximate cross-validation method for choosing the hyper-parameters which affect the performance of the proposed approach. The proposed method is evaluated through simulations using the artificial example.

Semiparametric support vector machine for accelerated failure time model

Chang Ha Hwang,Joo Yong Shim 한국데이터정보과학회 2010 한국데이터정보과학회지 Vol.21 No.4

For the accelerated failure time (AFT) model a lot of effort has been devoted to develop effective estimation methods. AFT model assumes a linear relationship between the logarithm of event time and covariates. In this paper we propose a semiparamet-ric support vector machine to consider situations where the functional form of the effect of one or more covariates is unknown. The proposed estimating equation can be computed by a quadratic programming and a linear equation. We study the ef-fect of several covariates on a censored response variable with an unknown probability distribution. We also provide a generalized approximate cross-validation method for choosing the hyper-parameters which affect the performance of the proposed approach. The proposed method is evaluated through simulations using the arti cial example.

Partially linear support vector orthogonal quantile regression with measurement errors

Chang Ha Hwang 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.1

Quantile regression models with covariate measurement errors have received a great deal of attention in both the theoretical and the applied statistical literature. A lot of effort has been devoted to develop e ective estimation methods for such quantile regres-sion models. In this paper we propose the partially linear support vector orthogonal quantile regression model in the presence of covariate measurement errors. We also provide a generalized approximate cross-validation method for choosing the hyperpa-rameters and the ratios of the error variances which a ect the performance of the proposed model. The proposed model is evaluated through simulations.

Semiparametric support vector machine for accelerated failure time model

황창하,심주용 한국데이터정보과학회 2010 한국데이터정보과학회지 Vol.21 No.4

For the accelerated failure time (AFT) model a lot of effort has been devoted to develop effective estimation methods. AFT model assumes a linear relationship between the logarithm of event time and covariates. In this paper we propose a semiparametric support vector machine to consider situations where the functional form of the effect of one or more covariates is unknown. The proposed estimating equation can be computed by a quadratic programming and a linear equation. We study the effect of several covariates on a censored response variable with an unknown probability distribution. We also provide a generalized approximate cross-validation method for choosing the hyper-parameters which affect the performance of the proposed approach. The proposed method is evaluated through simulations using the articial example.

Partially linear support vector orthogonal quantile regression with measurement errors

황창하 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.1

Quantile regression models with covariate measurement errors have received a greatdeal of attention in both the theoretical and the applied statistical literature. A lot ofeort has been devoted to develop eective estimation methods for such quantile regres-sion models. In this paper we propose the partially linear support vector orthogonalquantile regression model in the presence of covariate measurement errors. We alsoprovide a generalized approximate cross-validation method for choosing the hyperpa-rameters and the ratios of the error variances which aect the performance of theproposed model. The proposed model is evaluated through simulations.