Calculation of R^2 value for a non-linear regression

Question

I would first like to say, that I understand that calculating an R^2 value for a non-linear regression isn't exactly correct or a valid thing to do.

However, I'm in a transition period of performing most of our work in SigmaPlot over to R and for our non-linear (concentration-response) models, colleagues are used to seeing an R^2 value associated with the model to estimate goodness-of-fit.

SigmaPlot calculates the R^2 using 1-(residual SS/total SS), but in R I can't seem to extract the total SS (residual SS are reported in summary).

Any help in getting this to work would be greatly appreciated as I try and move us into using a better estimator of goodness-of-fit.

Cheers.

Perhaps math.stackexchange.com might be able to offer more assistance? — Aurum Aquila, Apr 13 '11 at 21:50
I just figured it out... sometimes asking a question, crystallizes things for you. `test.mdl<-nls(ctrl.adj~a/(1((conc.calc/x0)^b)), data=dataSet, start=list(a=100,b=10,x0=40), trace=T); # R^2 can then be calculated by: 1-(deviance(test.mdl)/sum((ctrl.adj-mean(ctrl.adj))^2))` I get the same r^2 as when using SigmaPlot, so all should be good. — sinclairjesse, Apr 13 '11 at 22:12
There's an old discussion on it here: https://stat.ethz.ch/pipermail/r-help/2002-July/023461.html — SiggyF, Apr 13 '11 at 22:14
@aule You should post your answer in the Answer box. Give yourself a little checkmark :) — mcpeterson, Apr 13 '11 at 23:07
@mcpeterson I will post the solution, but I'm new here and have to wait 24 hrs... — sinclairjesse, Apr 14 '11 at 14:23

score 12 · Accepted Answer · edited Jan 26 '18 at 22:19

12

Instead of extracting the total SS, I've just calculated them:

test.mdl <- nls(ctrl.adj~a/(1((conc.calc/x0)^b)),
                data=dataSet,
                start=list(a=100,b=10,x0=40), trace=T);

1 - (deviance(test.mdl)/sum((ctrl.adj-mean(ctrl.adj))^2))

I get the same R^2 as when using SigmaPlot, so all should be good.

edited Jan 26 '18 at 22:19

smci

32,567
20
113
146

answered Apr 14 '11 at 21:51

sinclairjesse

1,585
4
17
29

Seth · Answer 2 · 2013-11-04T18:10:43.393

5

So the total variation in y is like (n-1)*var(y) and the proportion not explained my your model is sum(residuals(fit)^2) so do something like 1-(sum(residuals(fit)^2)/((n-1)*var(y)) )

edited Nov 04 '13 at 18:10

answered Apr 14 '11 at 21:04

Seth

4,745
23
27

Calculation of R^2 value for a non-linear regression

2 Answers2