A Consequence of Non-orthogonal Data

Document Type

Article

Publication Date

1-7-1985

Abstract

With a non-orthogonal data structure and a multipart linear model, the partial sum of squares may exceed the sequential sum of squares. We attempt to impart an intuitive but rigorous understanding of how and why this phenomenon occurs. Using the model y=X0β0 + X1β1+X2β2+ε, where X0β0is always fit first, we show that the partial exceeds the sequential sum of squares in half of the space of possible observations, unless there is confounding. Thus when the problem is approached geometrically, the surprise is not that the phenomenon can occur, but that it does not happen more often. © 1985 Gordon and Breach, Science Publishers, Inc. and OPA Ltd.

Publication Source (Journal or Book title)

Journal of Statistical Computation and Simulation

First Page

51

Last Page

66

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