Is R-squared equivalent to mean squared error for non-linear regression As far to my knowledge r-squared should not be used in non-linear regression setup. Not only might the r2 be too high, but also the interpretation as the variance explained by the model might no longer be valid.
But looking at the mean squared error, it seems to be very similar. But it is said everywhere that mean squared error can be used in non-linear regression model. So my question is: is mse valid or should it also be considered not valid for non-linear regression?

I quote two sentences from Applied Linear Statistical Models (Kutner) that are relevant for the question.
p.525: the error sum of squares SSE and the regression sum of squares SSR do not necessarily sum to the total sum of squares SSTO. Consequently, the coefficient of multiple determination R2 = SSR/SSTO is not a meaningful descriptive statistic for non-linear regression.
p.528: For nonlinear regression, MSE is not an unbiased estimator of sigma2, but the bias is small when the sample size is large.
So unlike linear regression, the inference procedure for nonlinear regression based on MSE is only approximate, but it is good enough for large samples.
