I'm doing non-linear least squares iftting of TCSPC data and my residuals don't trend with my chi-squared values. IE a fit with unstructured residuals will have a chi-squared of ~0.54, but a fit with some remaining structure in the residuals will have a chi-squared ~0.96.
I would have expected their goodness or badness to vary together, but that doesn't seem to be the case. Which is generally most trustworthy?
I'm using the FluoFit software,for reference.
Thanks very much.
If residuals have a structure, there is something more than likely not accounted for in your model. You really should have them both. If I were reviewing a paper and I saw a residual plot with a pattern, I would be looking for an explanation of that for sure. The goal of regression tasks is to get to a point of random noise (i.e., random residuals), thus having an explanatory model. It would be possible to have a high chi-square, even if the residuals had a structure to them.
I can give you an example of this from a correlation task where r and the residuals were interestingly related. Student did a research project and had a very high r, but the residuals still had a structure, an indication that a better model existed. The example was with head impact coefficient (having to do with automobile safety and crash test mannequins). Student explored further and found the better model that removed the structure of the residual.
If residuals have a structure, there is something more than likely not accounted for in your model. You really should have them both. If I were reviewing a paper and I saw a residual plot with a pattern, I would be looking for an explanation of that for sure. The goal of regression tasks is to get to a point of random noise (i.e., random residuals), thus having an explanatory model. It would be possible to have a high chi-square, even if the residuals had a structure to them.
I can give you an example of this from a correlation task where r and the residuals were interestingly related. Student did a research project and had a very high r, but the residuals still had a structure, an indication that a better model existed. The example was with head impact coefficient (having to do with automobile safety and crash test mannequins). Student explored further and found the better model that removed the structure of the residual.
Thanks very much to both of you! This has been illuminating.
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis