Abstract
A method of sensitivity analysis is proposed for detecting influential observations in Hayashi's second method of quantification (discriminant analysis of categorical variables). It evaluates the changes of eigenvalues and the scores of categories due to a small change of the weights for a single or multiple individuals. The mathematical tool is the perturbation theory of eigenvalue problems which was used also in the investigations concerning Hayashi's third and fourth methods of quantification (Tanaka [14, 15, 16], Tarumi and Tanaka [17]). The perturbation theory used in the present paper covers not only the case where the eigenvalues of interest are all simple but also the case where there are some multiple eigenvalues among them.
