Sensitivity Analysis in Factor Analysis: Methods and Software

The present paper deals with methods and software of sensitivity analysis in some procedures of exploratory factor analysis. Our aim is to investigate how a small change of data affects the results of analysis. To do this Tanaka and Odaka(1989a,b,c) proposed methods of sensitivity analysis in principal factor analysis(PFA), maximum likelihood factor analysis(MLFA) and least squares factor analysis(LSFA), respectively. The major mathematical tools are influence functions for some functions of eigenvalues and eigenvectors of a real symmetric matrix. We treat the influence of omitting or downweighting one or more individuals on the estimates of the unique and common variance matrices \( \mathop \Delta \limits^ \wedge \) and \( \mathop {T*}\limits^ \wedge \), the precision of \( \mathop \Delta \limits^ \wedge \), and the goodness of fit.