1. Apart from "penalizing models of different parameters", What are other reasons for using Adjusted coefficient of determination (Adj.R2) in judging or evaluating linear and/or nonlinear models?
2. What other criteria for model evaluation are more robust and indicator of a better model than Adjusted coefficient of determination (Adj.R2)?
You will find the answer here-
http://blog.minitab.com/blog/adventures-in-statistics-2/why-is-there-no-r-squared-for-nonlinear-regression
and here...
http://statisticsbyjim.com/regression/r-squared-invalid-nonlinear-regression/
R^2 (adj) should be used in conjunction with (1) RMSE (root mean square error), which has the same physical units as that of the output/dependent variable, and also includes a penalizing term for number of model parameters (therefore allows to compare goodness of fit for models with different number of parameters), (2) the distribution of fit residuals.
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