Effects of Outlying Observations on Standard Errors in Factor Analysis

Standard errors (SEs) of an estimator are used to test the significance of specific parameters. Commonly used asymptotic SEs of the maximum likelihood estimator (MLE) are based on Fisher's information matrix or sandwich-type covariance matrix. When data contain outlying observations, the ML estimates can be biased and SEs may increase. It has been shown that when robust methods are used to minimize the effects of outlying observations, they lead to less biased estimators and better model assessments. However, effects of outlying observations on SEs have never been studied systematically under the framework of factor analysis. This thesis studies behaviors of SEs in three aspects: (1) The effects of different types of outlying observations on SEs of the MLE. (2) The behaviors of SEs of robust estimators. (3) Formulas for calculating asymptotic SEs of robust estimators are derived, in the case that replications are not implementable in practice. Moreover, these formulas are tested to see if they can estimate the true SEs well. Simulation is carried out under different conditions. Data containing different outlying observations and non-normally distributed data are generated and analyzed.