goodness of fit: Least absolute deviation

Hi,

I would like to know how matlab calculate sse, rmse and Rsquare when we used the options "Robust",'LAR' in fitoptions since the result I obtained is different from the traditional sse, rmse and Rsquare results.

Thanks

Elisabeth

Answer 1

[Tom Lane]

The function computes a robust estimate of the error standard deviation and calls this rmse. The sse is then dfe*rmse^2 where dfe is the degrees of freedom for the error term. Rsquare is 1-sse/sst.

A reference for the robust estimate of the error standard deviation is DuMouchel, W.H., and F.L. O'Brien (1989), "Integrating a robust option into a multiple regression computing environment," Computer Science and Statistics: Proceedings of the 21st Symposium on the Interface, American Statistical Association.

[Jérôme Elisabeth]

Thank's for your answer Tom.

Is it possible to have the way to compute those statistics as I couldn't find the reference on the internet.

Thanks

PS. here is my code to do the Robust fit weights:

s=fitoptions('Method','NonlinearLeastSquares','Algorithm','Levenberg-Marquardt','Weights',weights,'Robust','LAR','StartPoint',[308.56 2],'MaxFunEvals',10000,'MaxIter',4000);

g=fittype ('R10*exp(E0*((1/56.02)-(1/(x+46.02))))','options',s);

[g,gof,out]=fit(x,y,g);

[Shalini]

Can anyone tell me the significance of MaxFunEvals and MaxIter because, I increased these numbers to very high values but still after I evaluated my coefficients using Lavenberg Marquardt, I still got a better result after doing some manipulation after getting it out from matlab.Can anyone suggest the argument (MaxFunEvals,etc) values that should be given to get the highest accuracy?

[Sargondjani]

MaxFunEvals and MaxIter onyl halt the optimization when the maximum number of function evaluations or iterations are reached (when they bind)... if they were not reached when getting the solution, then increasing their numbers is not gonna improve accuracy.

i dont know which solver you use, but for most you can try smaller numbers for 'TolX', 'TolFun' instead (and 'TolCon' if applicable). This should improve accuracy...

(scaling your variables can also help)

[Tom Lane]

Jérôme, I may not quite understand. The function computes the rmse for you. The other statistics follow from the formulas I gave. If you want to see the code, look at the file private/statrobustsigma. If you need some information other than the code, send me e-mail.

[Dahhea Min]

Hi Tom,

Would it be possible to share the algorithm for this LAR or minimum absolute deviations?

Thanks,

Hannah