How can I get the CV% and Confidence interval for my parameter estimates from output of lsqnonlin function

Hi Everyone,

I want to calculate CV% and Confidence interval for my parameter estimates which I have estimated using lsqnonlin function.

[x,resnorm,residual,exitflag,OUTPUT,LAMBDA,Jacobian] =lsqnonlin(@compart_error , p0, [],[],optim_options,ob_conc3,ob_tPoints);

Here x is my parameter estimate with other outputs.

Any help will be greatly appreciated.

Thanks!

Answer 1

[Star Strider]

If you also have the Statistics Toolbox, use the nlparci function.

[Satish]

Thanks for the answer! Can you provide an example of how to use nlparci function using my output?

Thanks!

[Star Strider]

My pleasure!

Since lsqnonlin produces the Jacobian (the ‘Jacobian’ variable in your code), the parameter vector ‘x’ (in your code) and ‘residual’ (the vector of residuals in your code), you would use the alternate syntax. This is the usual way of calculating the parameter confidence intervals using Optimization Toolbox function parameter estimates and Statistics Toolbox statistics functions.

The documentation explains it better than I can:

• ci = nlparci(beta,resid,'jacobian',J) is an alternative syntax that also computes 95% confidence intervals. J is the Jacobian computed by nlinfit. If the 'robust' option is used with nlinfit, use the 'covar' input rather than the 'jacobian' input so that the required sigma parameter takes the robust fitting into account.

Note that the Statistics Toolbox functions such as nlparci require output of the sort that the nlinfit function produces. (It can fit only a single dependent variable.) Since I don’t know anything else you did (other than the line you quoted) or the model you fitted, I cannot guarantee that nlparci will work in your application.

[Satish]

Thanks a lot!

[Star Strider]

My pleasure!