impact of removing outliers in principal component analysis: a Monte Carlo study

ABSTRACT

Based on Bahnassys work [1989] to detect outliers in Principal Component Analysis; a simulation study has been conducted to explore the effect of removing outliers in Principal Component Model. Bahnassy's method mentions that if variables are standardized, the Pearson product moment correlation equals the average of the cross products. For each observation, the average over the [p[p-l]/2] correlations of the deviation squared of its cross products from the elements of the correlation matrix was computed. Observations with large deviations [D[k]] are defined as outliers. This method was applied to simulated data sets from normal distributions and from distributions with binary variables added. In some instances removing outliers causes the number of eigenvalues greater than one to change and changes the importance of some variables in each factor. Besides, the number of components were changed. These changes depend on number and type of variables sampe size, type of correlation matrix, and number of outliers in the data