Convergence Properties of Certain Minres Algorithms.
Levin (1988) has challenged the convergence properties of the Harman and Jones (1966) method of Minres factor analysis. Levin claimed that convergence of the Harman and Jones method is not guaranteed and that a modified version of this method, with proven convergence, is to be preferred. In the present article it is shown that both claims are invalid. Monotone convergence of the Harman and Jones method is guaranteed whereas the modified version, proposed by Levin, may converge to an incorrect solution. Levin has also claimed that the rank-one version of the Harman and Jones method, as implemented in a method by Zegers and ten Berge (1983) lacks a valid convergence proof, and that a method suggested by Comrey and Ahumada (1964, 1965) should be used instead. It is shown that these claims, too, should be reversed.
An efficient algorithm for joint correspondence analysis
Joint correspondence analysis is a technique for constructing reduced-dimensional representations of pairwise relationships among categorical variables. The technique was proposed by Greenacre as an alternative to multiple correspondence analysis. Joint correspondence analysis differs from multiple correspondence analysis in that it focuses solely on between-variable relationships. Greenacre described one alternating least-squares algorithm for conducting joint correspondence analysis. Another alternating least-squares algorithm is described in this article. The algorithm is guaranteed to converge, and does so in fewer iterations than does the algorithm proposed by Greenacre. A modification of the algorithm for handling Heywood cases is described. The algorithm is illustrated on two data sets.
An improvement of the Harman-Fukuda-method for the minres solution in factor analysis
The method proposed by Harman and Fukuda to treat the so-called Heywood case in the minres method in factor analysis i.e., the case where the resulting communalities are greater than one, involves the frequent solution of eigenvalue problems. A simple method to treat this problem requiring less computing time and enjoying higher numerical stability is described in this paper.