Isolating Change And Invariance In Patterns Of Behavior

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Abstract
General approaches which may be taken in the study of change and in- variance in patterns of behavior are presented and compared. These are classified according to whether data are gathered by "ideal" means, in which the same entities are assessed with the same measuring devices on several occasions, or data are gathered by "less-than-ideal" means, in which change of occasion is confounded with change in the sample of entities or is confounded with change in the sample of measuring devices. Several estimation and hypothesis-testing procedures are presented as appropriate for use with data gathered in one or the other of these ways. These include Tucker's multi-mode factoring technique, his inter-battery factoring procedure, Meredith's methods for rotating to achieve factorial invariance and various techniques of use in evaluating the significance of difference of vectors and matrices. Newly developed least-squares techniques, based in part upon discriminant function principles, are presented in some detai...