Which model is the best?

[spichal]

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

[Ksharp]

Calling @Rick_SAS

[Rick_SAS · Accepted solution]

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. 

[spichal]

Thanks for your really helpful advice.

Ludek