Robust factor analysis and an application

Factor Analysis is a multivariate analysis technique that has become popular in recent years. Factor Analysis aims to determine the dataset's original variables in a smaller number of derived (hypothetical) variables, known as factors, through linear combinations of these variables. This is achieved by making the covariance or correlation matrix of the original variables well-suited. An outlier is a data point or observation that behaves differently or takes on a much larger or smaller value than the other data points in a dataset (or data matrix). The presence of outliers in a dataset can also affect the assumption of multivariate normality, which is a common distribution of factors. When outliers are detected in a dataset, the covariance or correlation matrix can't be used for estimation. This will result in doubts about the reliability of the estimates made. In such cases, it is recommended to use robust multivariate location and scale measures when there are doubts about these measures. In multivariate techniques, the concept of robustness relates to using distance measures to control the different weight values given to observation values. This study aims to compare the performance of statistical techniques used in classic and robust factor analysis through simulation. The comparison criteria are total variance explained ratio and Rfit values. The performance of classical factor analysis techniques such as MLE (Maximum Likelihood), PCA (Principal Components), OLS (Ordinary Least Squares), WLS (Weighted Least Squares) and GLS (Generalized Least Squares) and robust factor analysis techniques such as MVE (Minimum Volume Ellipsoid), MCD (Minimum Covariance Determinant), M-estimator, S-estimator, SDE (Stahel-Donoho Estimator) and OGK (Orthogonal Gnanadesikan Kettenring) are compared. When considering the simulation results, it has been found that MLE and GLS methods perform better than others in classical factor analysis. On the other hand, when examining the simulation results for robust factor analysis, it was observed that MCD and M methods provide better results than the others. Two applications were made from real-life applications.