Thread Subject: confidence intervals for weighted nonlinear fit

Are confidence intervals from weighted fits meaningful?

I have been using lsqnonlin to fit my data and have been getting the confidence intervals using nlparci on the Jacobian returned by lsqnonlin. Now that I am weighting my data I'm not sure if this is still appropriate.

More specifically, I am fitting a change over time to get rates for various conditions. Eventually I want to fit my rates to a function that accounts for these conditions. To do this I want to weight by how much I trust my rates, but my rates themselves came from weighted data.

How can I combine my confidence in my data with my confidence in my original fits for a second fit?

John wrote:
> Are confidence intervals from weighted fits meaningful?
>
> I have been using lsqnonlin to fit my data and have been getting the confidence intervals using nlparci on the Jacobian returned by lsqnonlin. Now that I am weighting my data I'm not sure if this is still appropriate.

John, this demo

<http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/wnlsdemo.html>

touches on that subject, though it assumes you have the Statistics Toolbox. Hope it helps.

- Peter Perkins
  The MathWorks, Inc.