R2 limitation for linearity and monotonic? I'm studying sensitivity analysis.
I know that to use PCC and SRC, linearity and/or monotonic must be assumed.
So I'm trying to calculate R² for this, and my question for this is:

*

*Can I use GLM to calculate R²?

*Is there a lower bound on the R² value to assume that the model is linear or monotone?

thank you

*

*GLMs don’t usually care about square loss, so $R^2$ is of limited use. You’re always allowed to calculate a sum of squares, but it might not be meaningful.

UCLA has a nice page on $R^2$-style metrics for logistic regression. The McFadden variant is how I would think about it: as a ratio of loss functions (or likelihoods).


*$R^2$ can be very low without violating linearity, and $R^2$ can be very high without having linearity. For the former, imagine $\hat y_i =x_i+\epsilon_i$ with a very high variance for each $\epsilon_i$. For the latter, imagine slight curvature, such as a $y_i=x_i^3+\epsilon_i$ With a low variance for each $\epsilon_i$. Add in some lower-order polynomial terms to make that non-monotonic, if you want.

