Thurstone's analytical method for simple structure and a mass modification thereof

The analytical method for simple structure proposed by Thurstone is applied to four separate cases and found to yield satisfactory results. The simple structure obtained by Thurstone's method is found to match closely that obtained by other methods and corresponds to the true structure of the matrix in those cases where true structure is known. Difficulties about the choice of the correct trial vector led the writer to develop a modification of Thurstone's method, useful where high speed computational facilities are available. Instructions are given for this so-called mass modification, and the procedure is illustrated with a 5-factor, 14-variable example. While the results do not fully correspond to a previous graphical solution, it can be argued that the results obtained by the new method show an improved simple structure. The modified method is applied to three other correlation matrices, yielding in each case a satisfactory simple structure.Contribution No. 961 from the Department of Entomology, University of Kansas, Lawrence, Kansas.Most of the work on which this paper is based was performed during the summer of 1956 when the author was the holder of an Elizabeth Watkins Faculty Scholarship granted by the Kansas University Endowment Association. The work was carried out at the University of Illinois, where the author was privileged to spend the tenure of this scholarship. The writer is indebted to Professor L. H. Lanier, the Chairman of the Psychology Department, who graciously placed space and equipment at his disposal, and to Professor Raymond B. Cattell for his continuing encouragement of and interest in the author's work. Some of the computations were performed on the ILLIAC digital computer. The many courtesies extended by Professor J. J. Nash, Director of the Digital Computer Laboratory of the University of Illinois, are gratefully acknowledged. The writer is indebted to Mr. John R. Hurley for much assistance during the development of the computational routines and for a critical reading of this paper. Expenses in connection with the work were met by a General Research Grant of the University of Kansas.