PROCEDURES FOR WEIGHTING FACTORS AND VARIABLES IN ORTHOGONAL CONFIRMATORY FACTOR ANALYSIS

Much has been written on the subject of orthogonal confirma- tory factor analysis since Green's (1952) paper-the first dealing with this problem. Using the procrustean or residual least- squares criterion (to be minimized) of the sum of squared discrep- ancies between elements of the target or hypothesis matrix and those of the best fit, Fischer and Roppert (1964) and Kristof (1964) presented solutions essentially the same as Green's, although Green's solution required both the target and the matrix being transformed to be of full column rank. Schonemann's (1966) solution was most general in that it allowed both of these matrices to be of less than full rank. C1iff (1966) arrived at a slightly less general solution than Schonemann's, but one that was, for practical purposes, identical, although Cliff's criterion (to be maximimized) was different, and not least-squares. Cliff's solution, never- theless, satisfied the least-squares criterion. Gibson (1960, 1962) and Johnson (1966) addressed the related problem of obtaining least-squares orthonormalnizations of oblique transformation matrices. Techniques for rotating a given matrix orthogonally to a least-squares fit to an only partially specified target were outlined by Lawley and Maxwell (1964) and Browne (1970).