TITLE:
An Alternative Approach to AIC and Mallow’s Cp Statistic-Based Relative Influence Measures (RIMS) in Regression Variable Selection
AUTHORS:
Umeh Edith Uzoma, Obulezi Okechukwu Jeremiah
KEYWORDS:
Relative Influence Measure (RIM), BIC, AIC, Mallow’s Cp Statistic, Cook’s Distance
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.1,
February
23,
2016
ABSTRACT: 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 Cp 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.