Another (*very* similar) framework is item response theory. The model you're using would correspond to what’s called a 2PL model, named because it has two parameters: difficulty and discrimination. IRT difficulty measures the difficulty of an item and corresponds to difficulty in your model; IRT discrimination measures how sharply an item distinguishes between individuals near a given ability level and corresponds to the slope in your model. In the 2PL model, the probability of a person answering an item correctly is , very similar to your model.
Another (*very* similar) framework is item response theory. The model you're using would correspond to what’s called a 2PL model, named because it has two parameters: difficulty and discrimination. IRT difficulty measures the difficulty of an item and corresponds to difficulty in your model; IRT discrimination measures how sharply an item distinguishes between individuals near a given ability level and corresponds to the slope in your model. In the 2PL model, the probability of a person answering an item correctly is
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