#DFIND OUTLIERS IN HIGH DIMENSION HOW TO#

Similarly DFFITS can be calculated without repeated regressions as shown by Property 2. Values of CookвЂ™s distance of 1 or greater are generally viewed as high. This definition of CookвЂ™s distance is equivalent to Furthermore, CookвЂ™s distance combines the effects of distance and leverage to obtain one metric. Observation: Property 1 means that we donвЂ™t need to perform repeated regressions to obtain CookвЂ™s distance. Property 1: CookвЂ™s distance can be given by the following equation: Whereas CookвЂ™s distance is a measure of the change in the mean vector when the ith point is removed, DFFITS is a measure of the change in the ith mean when the ith point is removed. Where Е· j(i) is the prediction of y jby the revised regression model when the point ( x, вЂ¦, x ik, y i)В is removed from the sample.ДЄnother measure of influence is DFFITS, which is defined by the formula For the ith point in the sample, CookвЂ™s distance is defined as A measure of this influence is called CookвЂ™s distance. Points that have the most influence produce the largest change in the equation of the regression line. For our purposes now, we need to look at the version of the studentized residual when the ith observation is removed from the model, i.e.Дefinition 2: If we remove a point from the sample, then the equation for regression line changes. We will use this measure when we define CookвЂ™s distance below. A rule of thumb (StevenвЂ™s) is that values 3 times this mean value are considered large.ДЄs we saw in Residuals, the standard error of the residual e iВ isДЄnd so the studentized residuals s ihave the following property: Where there are k independent variables in the model, the mean value for leverage is ( k+1)/ n. Leverage measures how far away the data point is from the mean value. Observation: Where there is only one independent variable, we have Thus the strength of the contribution of sample value y iВ on the predicted value Е· i is determined by the coefficient h ii,В which is called the leverage and usually abbreviated as h i. Where each h ijonly depends on the x values in the sample. Leverage вЂ“В By Property 1 of Method of Least Squares for Multiple Regression, Y-hat = HY where H is the n Г— n hat matrix =. Points with large residuals are potential outliers. Is the measure of the distance of the ith sample point from the regression line. for the general population, there is nothing unusual about a 6-foot man or a 125-pound man, but a 6-foot man that weighs 125 pounds is unusual.Дefinition 1: The following parameters are indicators that a sample pointВ ( x i1, вЂ¦, x ik, y i)В is an outlier: Keep in mind that since we are dealing with a multi-dimensional model, there may be data points that look perfectly fine in any single dimension but are multivariate outliers.

#DFIND OUTLIERS IN HIGH DIMENSION HOW TO#

We now look at how to detect potential outliers that have an undue influence on the multiple regression model.

Dfind outliers in high dimension