Influential observations in factor analysis
Abstract of thesis entitled ?nfluential observations in factor analysis?
submitted by Kwan Chi-Wai
for the degree of Doctor of Philosophy
at the University of Hong Kong in January 1998.
The sensitivity analysis in factor analysis based on the influence curve and the local influence methods are discussed. The influence curves for the initial and rotated loadings are derived and compared. The consistence, the advantages and the limitations of the empirical and sample influence curves methods for the initial and rotated loadings are discussed. Internal and external norms as scalar influence measures for the vector-valued influence curves are introduced. The influence curves for the unique variances and the initial and rotated loadings are decomposed into two informative parts ?the factor scores and the residuals. The linearity and the decomposition of the influence curves enable us to derive some properties of the influence curves. Some relation of the influence of an observation to the magnitudes of the factor scores and residuals are revealed. The bounds, the equality of the empirical and sample influence curves, the conditions for the switching of the initial factor loadings and some other properties are stated and proved. The differences between applying the covariance and correlation matrices in deriving the influence curves for various parameters are obtained. The likelihood displacement and the influence curves for other statistics are also applied and their properties are studied. The appropriateness of the local influence based on the normal curvature and the slope for object functions other than the likelihood displacement are studied. The
formulas of the normal curvature for the local influence in specifically restricted statistical models are derived and applied to factor analysis. A slope approach of a modified likelihood displacement is also applied and compared with the curvature approach.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Date of Publication:01/01/1998