Hello,
the matlab code of estimated parameters of an nonlinear differential equation model in the added file is
options=optimset('MaxFunEvals', 10000, 'MaxIter', 10000, 'TolFun', 0.0001, 'TolX',0.0001,'Display','on');
[k_optim, resnorm, residual, exitflag, output, lambda, jacobian] = lsqnonlin(f,k0,lb,ub,options);
From a theoretical point of view: Can I use the Jacobian matrix from my output to perform what is called Principal Component Analysis for the world of linear regression models? For those models you use the covariance Matrix of the observables, because this appears in the equation for the Variance of the parameters. In case of nonlinear Models the parametervariance is defined as J_T * J (but Im not sure), so I thought I might could use the one from my output. Is anyone sure and knows code in Matlab to do this? Alternatively you might have other suggestions for dimension reducing techniques or methods of determining the extent of collinearity between parameters.
The code refers to a set of 240 measurements of y at z=0 and y at z=end of a tube, in which the chemicals at the beginning of the added file are flowing along and reacting according to the reaction laws r. The parameters k,K, EA and dH are supposed to be estimated, while the others are externally given. They are estimated by simulating the equation dy/dz with the ode45 solver in matlab. This is written in the file f which is used by the lsqnonlin command mentioned in the code above.
the matlab code of estimated parameters of an nonlinear differential equation model in the added file is
options=optimset('MaxFunEvals', 10000, 'MaxIter', 10000, 'TolFun', 0.0001, 'TolX',0.0001,'Display','on');
[k_optim, resnorm, residual, exitflag, output, lambda, jacobian] = lsqnonlin(f,k0,lb,ub,options);
From a theoretical point of view: Can I use the Jacobian matrix from my output to perform what is called Principal Component Analysis for the world of linear regression models? For those models you use the covariance Matrix of the observables, because this appears in the equation for the Variance of the parameters. In case of nonlinear Models the parametervariance is defined as J_T * J (but Im not sure), so I thought I might could use the one from my output. Is anyone sure and knows code in Matlab to do this? Alternatively you might have other suggestions for dimension reducing techniques or methods of determining the extent of collinearity between parameters.
The code refers to a set of 240 measurements of y at z=0 and y at z=end of a tube, in which the chemicals at the beginning of the added file are flowing along and reacting according to the reaction laws r. The parameters k,K, EA and dH are supposed to be estimated, while the others are externally given. They are estimated by simulating the equation dy/dz with the ode45 solver in matlab. This is written in the file f which is used by the lsqnonlin command mentioned in the code above.
Attachments

60 KB Views: 2