Quote Originally Posted by Rudeofus View Post
Splines are commonly used to describe arbitrarily curved shapes, because they can be made to fit almost any point set with a smooth looking curve. In the same fashion you can make them LMS fit a point cloud, and that's what you did with your LOESS approach, or to say it more accurately: that's what the LOESS algorithm did for you. The more degrees of freedom you allow the LOESS algorithm, the closer the result will fit your point cloud, but remember that your point cloud is still noisy data!
Rudi, you make a very good point, and I have no doubt that spending more time writing code that would fit a more correct curve, which follows the log relationship which you, and David, have mentioned, would be a better way to get accuracy. However, my original goal was to calculate the CI in a more automated way than what I did previously using graph paper, having picked the technique from Bill (thanks!). When doing it by hand, I already had to create a "spline" by rotating the French curve (Bezier) two or three times, as I was drawing a smooth line through my points plotted off the densitometer. Then I was using the CI-ruler to approximately find the 3 points that met the condition. I have a feeling that the Bezier spline approximation, calculated in my code, does as good, or perhaps even a better job that what I did by hand. Perhaps you have a set of logE/D points for which you know their CI, that we could use to further test my code? I wonder how much more (useful) precision would I gain by finding a better, more "film-like" log-based smoother.

Quote Originally Posted by dpgoldenberg View Post
I'm glad to hear that my suggestions were helpful and that you were able to implement them in R. You might want to try fitting your data to the function I suggested in the earlier thread:

D(x) = a1*ln(1+exp(a2*x + a3))
where D is density, x is exposure (on a logarithmic scale) and a1,a2, a3 are constants. ln is the natural logarithm and exp is the number e raised to the power in the parentheses.
Many thanks, David and Rudi, for your suggestions—I wonder what would be able to cope with a touch of shouldering, should it be present. I will use them the next time I have a chance to spend a day coding film-testing utilities.