Influential Observations and Cutoffs of Different Influence Measures in Multiple Linear Regression

Abstract

The analysis of data for outliers is a part of model building and data summarizing for model testing, parameter estimation, prediction and peculiarity investigations. Any influential point can disproportionately pull the ordinary least squares line and distort the predictions. Thus the detection of outlying observations is very essential in the course of model building in various disciplines, such as, medical research, economics, sociology, computer science, etc. A point is an influential one if it causes dramatic change in the model after its deletion. Each of the available test statistics has different cutoff values that indicate the amount of outlyingness. Sometimes only one statistic is sufficient to provide the information about influential points but often it is necessary to examine the cutoff of more than one influence measure. The reason behind is that all the cutoff values are either a function of the sample size or number of predictors or both. Also validity of the cutoff value is subjected to some additional conditions. In this paper we try to critically examine those conditions with the help of simulation study. We shall use a few combinations of (n,k) , where n is the sample size and k is the no. of outliers for assessing the performances.