Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Multivariate Data Modeling Multiple Regression Variance Inflation Factor  
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Variance Inflation FactorThe Variance Inflation Factor (VIF) is a means to detect multicollinearities between the independent variables of a model. The basic idea is to try to express a particular variable x_{k} by a linear model based on all other independent variables. If the calculated model shows a high reliability (i.e. the goodness of fit is high) the tested variable x_{k} is likely to be (multi)collinear to one or more of the other variables.In general, the VIF is calculated for all independent variables of a model. In a second step the variables showing the greatest values are removed from the model. As a rule of thumb, the VIF of all variables should be less than 10 in order to avoid troubles with the stability of the coefficients. From a mathematical point of view, the VIF measures the increase of the variance in comparison to an orthogonal basis. The VIF of the kth variable is defined by the following formula: VIF_{k}= 1/(1r_{k}^{2}), where r_{k}^{2} is the goodness of fit of the linear model for x_{k} based on all other variables.


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