Analysis of Covariance after Nonlinear Least-Squares Fitting

@article{citeulike:1392923, abstract = {After linear least-squares fitting (multiple regression) of a number of parameters, tests of significance of fitted parameter values may involve repeating the fit with various combinations of parameters omitted (i.e. forced to have zero values). This is often inappropriate in the nonlinear case for two reasons: (i) zero may not be a reasonable value for an ill-determined parameter, and (ii) the cost of doing additional fits may be prohibitive. Also, it can be difficult to automate the process of rejecting ill-determined parameters in cases where, because of high correlation, some of them, all of which are apparently ill determined, have in fact one or more well-determined combinations. Such cases are by no means rare in some applications, for example fitting of rate coefficients to mass-action kinetic data. A method is described for automatic decision-making in this case, based on a multiparameter least-squares fitting process.}, author = {Curtis}, citeulike-article-id = {1392923}, journal = {IMA Journal of Numerical Analysis}, keywords = {covariance, estimator, least, squares, statistics}, posted-at = {2007-06-16 01:01:14}, priority = {4}, title = {Analysis of Covariance after Nonlinear Least-Squares Fitting}, url = {http://imajna.oxfordjournals.org.proxy.lib.sfu.ca/cgi/reprint/6/4/453} }

TY - JOUR ID - citeulike:1392923 L3 - citeulike-article-id:1392923 TI - Analysis of Covariance after Nonlinear Least-Squares Fitting JF - IMA Journal of Numerical Analysis N2 - After linear least-squares fitting (multiple regression) of a number of parameters, tests of significance of fitted parameter values may involve repeating the fit with various combinations of parameters omitted (i.e. forced to have zero values). This is often inappropriate in the nonlinear case for two reasons: (i) zero may not be a reasonable value for an ill-determined parameter, and (ii) the cost of doing additional fits may be prohibitive. Also, it can be difficult to automate the process of rejecting ill-determined parameters in cases where, because of high correlation, some of them, all of which are apparently ill determined, have in fact one or more well-determined combinations. Such cases are by no means rare in some applications, for example fitting of rate coefficients to mass-action kinetic data. A method is described for automatic decision-making in this case, based on a multiparameter least-squares fitting process. KW - covariance KW - estimator KW - least KW - squares KW - statistics AU - Curtis UR - http://imajna.oxfordjournals.org.proxy.lib.sfu.ca/cgi/reprint/6/4/453 ER -