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to Structural Equation Modeling
There were some questions as to how to do IRT and calculate the difficulties and discriminations in lavaan. This was a bit more work than I expected, as it seems that lavaan's default minimization gave me a local minimum in a data set which had missing data. I outline what seemed to work, but on the whole, Mplus runs fine in comparison and unless you're checking it, there's no way to know if lavaan found the global minimum.