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One way you could (I won't say should) constrain all the observed sets of predictions to be non-negative is to use Sequential Quadratic Programming (SQP). To explain how SQP works, we can backstep to thinking about how Newton's method works. One way to view it is we make a quadratic approximation of the function given the current derivatives. Quadratic ...


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I am going to assume you want a link function on the open interval $(-1,1)$, since you want this to map continuously onto the real numbers. There are infinitely many monotonic link functions $g: (-1,1) \rightarrow \mathbb{R}$ that map from your desired domain to the set of all real numbers. Taking the function to be strictly increasing, every link function ...


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