Abstract
This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.
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Much of the work on this paper was completed while the author held a U.S.P.H.S. Postdoctoral Fellowship at Yale University (1964–65). Many of the ideas in this paper have been discussed in the author's doctoral dissertation which was submitted to Yale University in 1965.
Special thanks are due to Robert P. Abelson for his encouragement and for many helpful and stimulating discussions about problems which arose in the preparation of this paper. I would also like to thank Francis J. Anscombe and Alan T. James for their valuable suggestions and constructive criticism of an earlier draft of this article.
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Gollob, H.F. A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika 33, 73–115 (1968). https://doi.org/10.1007/BF02289676
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DOI: https://doi.org/10.1007/BF02289676