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Biometrika 1995 82(2):411-417; doi:10.1093/biomet/82.2.411
© 1995 by Biometrika Trust
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MISCELLANEA

Curvature measures for multiresponse regression models

M. GUAY

Department of Chemical Engineering, Queen's University Kingston, Ontario, Canada, K7L 3N6

The Bates & Watts (1981) curvature measures developed for single response nonlinear least squares problems are extended to multiresponse parameter estimation problems based on the Box-Draper estimation criterion. Exact determination contours are approximated by contours of the generalised least squares model conditioned on the maximum likelihood estimate of the covariance matrix for the responses. By this approximation, curvature measures calculated for the generalised least squares can be related to the determinant contours. The assessment of nonlinearity for a multiresponse model presented in this study is two-fold. First, a nonuniformity measure is developed to measure the validity of the approximation of the determinant contours by generalised least squares contours. Secondly, curvature measures similar to those of Bates & Watts are calculated for the generalised least squares model to evaluate the validity of the linear approximation of the model functions in a neighbourhood of the parameter estimates.

Key Words: Box-Draper estimation • Multiresponse regression • Nonlinear parameter estimation


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