is the R-square can be adopted as a measure for goodness of fit for the non linear regression relationship between the response and independent variables.
Dear Sir,
R-square- It give best fitness between dependent and independent parameters of a model (linear and non linear regression analysis). It's ideal value is 1 (or 100%).
RMSE value- It is error of a model. Higher the R-square value and least the RMSE value are give the model best fit in regression analysis.
R-square does not give indication about nonlinear regression modelling, just deal with linear models, for non-linear model you must check the goodness of fit by diagnostic plots of residual
Abbas, why should R² not be used for non-linear regression? If the fit is obtained by minimizing the residual variance, it should not matter if the underlying model is linear or non-linear.
What do you mean with "non-linear"? A non-linear predictor (e.g. x^2) in a linear regression model (intrinsically linear model)? Then R can tell you something about the goodness of fit. Otherwise, in an intrinsically non-linear regression, the minimum of SSR (sum of squared residuals) can not simply be calculated but has to be estimaed through an interative process. If this is done, again R can be calculated.
Dear Amjab,
I suggest the book "Bates and Watts Non-linear regression analysis and its applications, 1988. 365 p".
When you fit a non-linear model with more than 3 parameters, for example, using Linear Least Squares, you will see that the most non-linear parameter has significant asymmetry and bias. The R2 calculated by some softwares is, sometimes, 97%. Look the parameters estimates, they do not make sense as they have to make when we choose a non linear model. Best regards. Walter
R-squared is called the coefficient of determination of the model. It is interpreted as the proportion of the variability in the dependent explained by the independent variable(s) irrespective of whether the model is linear or non-linear. It is therefore a measure of goodness-of-fit. There is no absolute measure of goodness-of-fit. Therefore goodness-of-fit is tested not with just a single measure like the R-squared alone, but also with other measures like the RMSE (as mentioned by Kundan above), the Akaike Information Criterion(AIC), Bayesian Information Criterion(BIC), Schwarz Information Criterion(SIC), Hannan-Quinn Criterion, etc.
Greeting,
I agree with abbas. I think that, R squared is not suitable for fitting Non-linear models because R squared not same desirable properties as in the linear-model case.
"If there is no linear relationship between the two variables, the correlation coefficient [r] is close to 0. [This] does not mean that there isn't any type of relationship between two variables; it is possible for two variables to have an r of 0 and be strongly related in a non-linear way".(Quote from http://ask.metafilter.com/65278/Statistics-tell-me-about-rsquare-for-nonlinear-models).
So, I suggest using another Criterion as Akaike Information Criterion.
See this paper please
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892436/
Huda
Various pseudo r-squared measurements are used for nonlinear models and other models where r-squared is not defined. They cannot be interpreted as directly analogous to r-squared, but are useful. Note that different ones are calculated differently, and so are not comparable to one another.
There's a short description here
http://rcompanion.org/handbook/G_10.html
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