Variable selection in multiple linear regression: The influence of individual cases

Steel, S. J.; Uys, D. W.

doi:10.5784/23-2-52

Cited by 4 publications

(9 citation statements)

References 24 publications

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“…As proposed by [3], the influence measure for the th i case when the Cook's distance is used becomes…”

Section: Cook's Distance and The Influence Measurementioning

confidence: 99%

“…This is equivalent to selecting the variables which maximize a penalized version of the maximum log-likelihood. As proposed by [3], the influence measure for the th i case when the AIC criterion is used becomes…”

Section: Rss V N N −mentioning

confidence: 99%

“…Only few papers dealing with the influence of individual data cases in regression explicitly take an initial variable selection step into account. This problem is handled by [3]- [6].…”

Section: Introductionmentioning

confidence: 99%

“…One objective of regression variable selection is to reduce the predictors to some optimal subset of the available regressors [3]. In literature, several approaches of variable selection exist, which include the stepwise deletion and subset selection.…”

Section: Introductionmentioning

confidence: 99%

“…When the detected outliers are removed, the standard least angle regression is applied on the cleaned data to robustly sequence the predictor variables in order of importance. [3] proposed a method called the Relative Influence Measure using the Mallow's p C and AIC Statistics. These methods are dimensionally consistent, computationally efficient and able to identify influential case, though, failed in asymptotic consistency.…”

Section: Introductionmentioning

confidence: 99%

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An Alternative Approach to AIC and Mallow’s Cp Statistic-Based Relative Influence Measures (RIMS) in Regression Variable Selection

Uzoma¹,

Jeremiah²

2016

OJS

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Outlier detection is an important data screening type. RIM is a mechanism of outlier detection that identifies the contribution of data points in a regression model. A BIC-based RIM is essentially a technique developed in this work to simultaneously detect influential data points and select optimal predictor variables. It is an addition to the body of existing literature in this area of study to both having an alternative to the AIC and Mallow's C p Statistic-based RIM as well as conditions of no influence, some sort of influence and perfectly single outlier data point in an entire data set which are proposed in this work. The method is implemented in R by an algorithm that iterates over all data points; deleting data points one at a time while computing BICs and selecting optimal predictors alongside RIMs. From the analyses done using evaporation data to compare the proposed method and the existing methods, the results show that the same data cases selected as having high influences by the two existing methods are also selected by the proposed method. The three methods show same performance; hence the relevance of the BIC-based RIM cannot be undermined.

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“…As proposed by [3], the influence measure for the th i case when the Cook's distance is used becomes…”

Section: Cook's Distance and The Influence Measurementioning

confidence: 99%

Section: Rss V N N −mentioning

confidence: 99%

“…Only few papers dealing with the influence of individual data cases in regression explicitly take an initial variable selection step into account. This problem is handled by [3]- [6].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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