Sensitivity Analysis in Canonical Factor Analysis

Abstract

ABSTRACTshows that a similar method can be developed also in canonical factor analysis.Two numerical examples are given for illustration.

Local Aspects of Sensitivity Analysis in Hayashi's Third Method of Quantification

“…There are many works on the sensitivity analysis in linear regresssion analysis; $elsley, Kuh, and Welsch (1980), and Cook and Weisberg (1982), among others. In a similar context, many tools of sensitivity analysis for multivariate methods are developed recently by Tanaka and his colleagues; see , Tanaka and Odaka (1988), and Tanaka and Tarumi (1988). In this study, we extend the results obtained by Tanaka (1984) for the sensitivity analysis in Hayashi's third method of quantification.…”

Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods

“…The approximate relative changes based on linear approximation, p(') and T(1), and those based on quadratic approximation, p(i) + (e/2)P(2) and T(1) + (e/2)T(2), analysis (LSFA) and alpha factor analysis (AFA) have a common property that an eigenvalue problem of a symmetric matrix is contained as a part in their determinating equations . Based on this property Tanaka and Odaka(1989a,b,c), Tanaka and Tarumi(1989) and have derived the influence functions for the unique and common variance matrices in PFA, MLFA, LSFA, CFA, and AFA, respectively, using the perturbation expansion of T discussed in section 5.2. Let us consider the case of PFA.…”

“…Using the expansions of certain functions of eigenvalues and eigenvectors obtained by Tanaka (1988), Tanaka and Odaka (1989a,b,c) and Tanaka and Tarumi (1989) have derived the influence functions for the unique and common variance matrices in various procedures of exploratory factor analysis. The same expansions are used to evaluate the changes of the configurations of principal components or factors with RV coefficients (Benasseni, 1990;Tanaka, 1990,1991).…”

Sensitivity Analysis in Principal Factor Analysis: A Numerical Investigation

“…Therefore, it may still be worth to study sensitivity analysis in noniterative and iterative procedures of PFA. We also consider sensitivity analysis in other factor analysis proce dures in separate papers (see Tanaka and Odaka, 1989b, c ;Tanaka and Tarumi, 1988).…”