Influence Measures in Ridge Regression

Walker, Esteban; Birch, Jeffrey B.

doi:10.1080/00401706.1988.10488370

Cited by 80 publications

(65 citation statements)

References 11 publications

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“…Diagnostic results in Box-Cox transformation model (Box and Cox, 1964) have also been done by Cook and Wang (1983), Hinkley and Wang (1988), Kim et al (1996), and Tsai and Wu (1990). Walker and Birch (1988) derived a version of Cook's distance in the ridge regression (Hoerl and Kennard, 1970), and Kim et al (2015) proposed a type of Cook's distance in the lasso regression model.…”

Section: Introductionmentioning

confidence: 99%

Case influence diagnostics for the significance of the linear regression model

Bae

Noh

Kim

2017

CSAM

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In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination R 2 and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in R 2 and F-statistic.

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Section: Introductionmentioning

confidence: 99%

Case influence diagnostics for the significance of the linear regression model

Bae

Noh

Kim

2017

CSAM

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“…Therefore, mixed estimation and ridge type regression are suggested to mitigate this effect. In addition to multicollinearity, the presence of influential observations in the observed data is seriously affected by the estimators as those estimators are not unbiased [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…Belsley [3] investigated the leverage in ridge regression. Walker and Bitch [2] studied the influence of observations in ordinary ridge regression estimator (ORRE) based on case deletion method. Shi [4] proposed the local influence in principal component analysis by defining a generalized Cook statistic and showed that his method is equivalent to Cook's approach under the likelihood framework.…”

Section: Introductionmentioning

confidence: 99%

“…In literature, many authors [1][2][3] noted that the influential observations on ridge type estimators are different from the corresponding least squares estimate and that multicollinearity can even disguise anomalous data. Belsley [3] investigated the leverage in ridge regression.…”

Section: Introductionmentioning

confidence: 99%

“…Shi [4] proposed the local influence in principal component analysis by defining a generalized Cook statistic and showed that his method is equivalent to Cook's approach under the likelihood framework. Shi and Wang [2] analyzed the influential cases in ORRE using local influence method. Jahufer and Chen [5] studied global influential observations in modified ridge regression estimator (MRRE) moreover, Jahufer and Chen [6] studied local influential observations in MRRE.…”

Section: Introductionmentioning

confidence: 99%

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Detecting Global Influential Observations in Liu Regression Model

Jahufer¹

2013

OJS

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In linear regression analysis, detecting anomalous observations is an important step for model building process. Various influential measures based on different motivational arguments and designed to measure the influence of observations on different aspects of various regression results are elucidated and critiqued. The presence of influential observations in the data is complicated by the presence of multicollinearity. In this paper, when Liu estimator is used to mitigate the effects of multicollinearity the influence of some observations can be drastically modified. Approximate deletion formulas for the detection of influential points are proposed for Liu estimator. Two real macroeconomic data sets are used to illustrate the methodologies proposed in this paper.

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Seasonal divergence in the sensitivity of evapotranspiration to climate and vegetation growth in the Yellow River Basin, China

Pei

et al. 2017

JGR Biogeosciences

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Seasonal variations in terrestrial evapotranspiration (ET) in the Yellow River Basin (YRB) have crucial impacts on the seasonal trajectories of the regional water cycle, vegetation growth, and local climate feedback. However, the possibly divergent roles of climate and vegetation growth variations in controlling seasonal ET patterns remain poorly quantified. This study therefore quantifies the interannual sensitivity and attribution of ET to climate and vegetation growth variations in different seasons and different biomes in the YRB in China between 1982 and 2011, using the satellite‐derived normalized difference vegetation index (NDVI), FLUXNET‐based upscaled ET, and concurrent climate data. The results reveal a clear seasonal divergence in the interannual sensitivity of ET to climate and vegetation growth variations in the YRB. Interannual precipitation and NDVI variations play a dominant role in controlling seasonal ET variations in the YRB, with temperature having a marginal effect. Interannual ET sensitivity to precipitation weakens with an increasing mean annual precipitation gradient in almost all seasons, especially in summer and autumn. More importantly, a seasonally varying role of vegetation growth in mediating seasonal ET was discovered, and a crucial role of late‐growing‐season vegetation growth in controlling the seasonal trajectory of regional ET was explicitly identified. These results suggest that ongoing intensive vegetation restoration has crucial impacts on seasonal water‐cycle patterns and consequent terrestrial‐atmospheric biogeochemical feedback in the YRB.

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Influence Measures in Ridge Regression

Cited by 80 publications

References 11 publications

Case influence diagnostics for the significance of the linear regression model

Case influence diagnostics for the significance of the linear regression model

Detecting Global Influential Observations in Liu Regression Model

Seasonal divergence in the sensitivity of evapotranspiration to climate and vegetation growth in the Yellow River Basin, China

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