In Part 1, we went through the simplest item response model, the 1PL model, from the perspective of simulations. Starting with item difficulty and testee ability, we worked forward to simulate item responses that mimic real-world data. Back then, we were precisely laying out the data generating process that is assumed by the item response theory. In this post, we work backward. We will start with the item responses and work back toward the unobserved difficulties and abilities, with the help of statistical …