Logistic Fit

[Han]

(01-22-2014 04:14 PM)Helge Gabert Wrote:  This looks good to me, and it works!

Another possibility would be to let the user specify starting values, along with the fit, and use something like the Levenberg-Marquardt method, in analogy to the Moda library (V1.52) on hpcalc.org for the HP49/50.

I'm not sure if you were referring to my post (the one about a "naive" approach to logistic fitting), but if you were, do keep in mind that this technique is quite limited. For example, if the data is such that the domain is restricted to the interval \( [1,5] \) and whose range is in the interval \( [.5,2] \) then this technique fails. If we normalize the range \( [.5,2]\) to \( [P_{min}, P_{max} ] \), how does one determine whether \( P_{min} \) is closer to 0 or .1 or .5 or even .75 (similarly if \( P_{max} \) should be 1, or much smaller). The domain may be of some help. That is, if we're "far to the right" then \(P_{min}\) and \( P_{max} \) will presumably be each closer to 1. However, there are similar issues even when using the domain.

So when you say have the user specify the starting values, would that be essentially the same as allowing them to select the \( P_{min} \) and \( P_{max} \) values? I think that could work for data that is not central about the origin.

I'm a little rusty in logistics modeling, but vaguely remember something about maximum likelihood estimates have some connection here (?).