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Can you use R-Squared for nonlinear?
R-squared seems like a very intuitive way to assess the goodness-of-fit for a regression model. Unfortunately, the two just don’t go together. R-squared is invalid for nonlinear regression. Consequently, it’s important that you understand why you should not trust R-squared for models that are not linear.
Why is R-Squared not valid for nonlinear regression?
Nonlinear regression is a very powerful analysis that can fit virtually any curve. Minitab doesn’t calculate R-squared for nonlinear models because the research literature shows that it is an invalid goodness-of-fit statistic for this type of model. There are bad consequences if you use it in this context.
What is the goodness of fit of a nonlinear function?
We have fitted a nonlinear function to observed data. The next step should be the assessment of the goodness of fit of this function (like R 2 for linear models). What are the usual ways to measure this?
How to check the goodness of a nonlinear distribution?
Perform a linear regression with independent variables A and B. Calculate distribution’s parameters from regression parameters. (The distribution is nonlinear and has variable C as an input.) Assess goodness of fit of nonlinear distribution by comparing estimated to observed data.
Which is the measure of goodness of fit?
For the standard linear regression model the familiar coefficient of determination, R-squared (R2) is a widely used goodness-of-fit measure whose usefulness and limitations are more or less known to the applied researcher. Application of this measure to nonlinear models generally leads to a measure that can lie outside the [0,1] interval and
Is it possible that none of your fits are the best?
Note that it is possible that none of your fits can be considered the best one. In this case, it might be that you need to select a different model. Conversely, it is also possible that all the goodness of fit measures indicate that a particular fit is the best one.