CORRESPONDENCE Algorithms

CORRESPONDENCE Algorithms The CORRESPONDENCE algorithm consists of three major parts: 1. A singular value decomposition (SVD) 2. Centering and rescaling of the data and various rescalings of the results 3. Variance estimation by the delta method. Other names for SVD are “Eckart-Young decomposition” after Eckart and Young (1936), who introduced the technique in psychometrics, and “basic structure” (Horst, 1963). The rescalings and centering, including their rationale, are well explained in Benzécri (1969), Nishisato (1980), Gifi (1981), and Greenacre (1984). Those who are interested in the general framework of matrix approximation and reduction of dimensionality with positive definite row and column metrics are referred to Rao (1980). The delta method is a method that can be used for the derivation of asymptotic distributions and is particularly useful for the approximation of the variance of complex statistics. There are many versions of the delta method, differing in the assumptions made and in the strength of the approximation (Rao, 1973, ch. 6; Bishop et al., 1975, ch. 14; Wolter, 1985, ch. 6). Other characteristic features of CORRESPONDENCE are the ability to fit supplementary points into the space defined by the active points, the ability to constrain rows and/or columns to have equal scores, and the ability to make biplots using either chi-squared distances, as in standard correspondence analysis, or Euclidean distances. reference:tutorial spss