Scree Plots,Data Structure,and Random Variance

Abstract

Data sets of known and predetermined structure (plasmodes) were created by the Monte Carlo method and subjected to exploratory factor analysis; the scree plots for each plasmode were then drawn. Since the aim of the paper is to give a graphic portrayal of the effects of orthogonality and random variance upon the scree plot, appropriate data sets were selected to illustrate these effects. A progression of scree plots is shown wherein it may be clearly seen how an increase in both nonorthogonality and random variance leads to the suppression of the factor structure in the data. Although this is a well known phenomenon, the visualization highlights the limitations of Kaiser's Eigenvalue > 1 rule and the scree test; it also illustrates the robustness of the factor analytic technique.