In Silico Comparative Evaluation of Classical and Robust Dimension Reduction for Psychological Assessment

The classic exploration of correlated multivariable psychological assessment data employs dimension reduction of the original p¬ variables to a lower q-dimensional space through principal component analysis (PCA). Standard criteria in the selection of the number of q dimensions may be affected by non-normal distributions and atypical observations. Performance of PCA was compared to robust dimension reduction techniques including Grid Projection Pursuit and robust covariance estimation (ROBPCA) in the accurate identification of the predetermined number of q-dimensions according to selection criteria for the cumulative proportion of variation, Kaiser-Guttman eigenvalue rule, and quantitative localization of Cattell’s scree plot ‘elbow’ via segmented regression. Based on in silico benchmarking using various simulated multivariate conditions, ROBPCA was consistent in correctly identifying the true q-dimensions. PCA can be improved through the adjustment of values for the cumulative proportion of variation and eigenvalue thresholds. Grid Projection Pursuit was the lowest performer among the techniques under simulated conditions.M.Sc