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The Use of Guided Reformulations when Collinearities are Present in Non- Linear Regression

Jeffrey S. Simonoff and Chih-Ling Tsai
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 38, No. 1 (1989), pp. 115-126
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2347686
Stable URL: http://www.jstor.org/stable/2347686
Page Count: 12
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The Use of Guided Reformulations when Collinearities are Present in Non- Linear Regression
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Abstract

Multicollinearity is as serious a problem in non-linear regression as it is in linear regression, with the vectors of partial derivatives taking the place of the columns of the design matrix. The solution to this problem is to reformulate the model, but this is often difficult. In this paper a guided reformulation procedure is developed based on the representation of collinearity in the model. Several examples are treated, and it is shown that the reformulation model generally has reduced collinearity and curvature with little loss of fit. A discussion of the relationship of collinearity to curvature for a certain class of non-linear models is provided. Potential difficulties with the procedure are also discussed.

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