ASSESSING THE STABILITY OF PRINCIPAL COMPONENTS USING REGRESSION

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to pre dict stability is devised, calibrated, and tested using simulated Norm al data. Results show that the model can provide useful predictions of individual principal component stability when working with correlatio n matrices. Further, the predictive validity of the model is tested ag ainst data simulated from three non-Normal distributions. The model pr edicted very well even when the data departed from normality, thus giv ing robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpr etability of principal components.