topic Re: Which model is the best? in Mathematical Optimization, Discrete-Event Simulation, and OR

Which model is the best?

spichal — Tue, 01 May 2018 19:17:13 GMT

Hi,

I would like to ask about one problem I need to solve. I had found codes for fitting logarithmic spiral and circle with measured data (R. Wicklin). Later I tried to compare these models with my own measured data (short arcs). In some cases, the plots of spiral and a circle (or ellipse) fitted very similar. By reading the programmes for spiral and a circle I realized that the codes optimize data in a different way. I would like to know if there is a way I could choose the best fitting model (according to the value of the objective function, radius or something else).

Thanks

Ludek

Re: Which model is the best?

Ksharp — Wed, 02 May 2018 14:02:21 GMT

Calling @Rick_SAS

Re: Which model is the best?

Rick_SAS — Wed, 02 May 2018 14:47:18 GMT

The simplest measure would be a statistic that uses the residuals. Either sum-of-squared errors (SSQ) or mean squared error (MSE) could be used. The difficulty, I think, is that the residuals ought to be computed in the direction orthogonal to the curve. For fitting a circle, this means that the residuals are in the radial direction. For ellipses and spirals, the definitions for the residuals are in the comments.

A more complex statistic would be an adjusted R-squared statistics, which includes a "penalty term" for fitting more complex models. A circle has two parameters, an ellipse has four parameters, and the spiral has four.

Re: Which model is the best?

spichal — Wed, 02 May 2018 20:21:26 GMT

Thanks for your really helpful advice.

Ludek