Identifying most influential observations in factor-analysis

At the mathematical level, a factor or principal component of a factor analysis is simply a linear combination of variables under some constraints. Therefore, as in regression analysis, there are conditions under which individual or joint observations can be influential in the sense that their presence or absence significantly influences the obtained values of the estimated factor loadings. The nature of these effects as well as potential effects due to ‘gross errors’ in the data set should be investigated in order to determine which observations, if any, need to be analyzed separately or excluded entirely. The purpose of this paper is (1) to propose a new technique for identifying influential observations and observations containing ‘gross errors’ and (2) to discuss situations under which each is likely to significantly alter the results of a factor analysis.