We have been working on a complicated IRT model designed for a mixture of discrete and continuous responses with zero-and-one inflation. The model also allows incorporating auxiliary variables via latent regression, and the code is designed to accommodate highly sparse datasets (e.g., there are 2700 items in total but each student only responds to six of them).
We just submitted the paper, and prepared this GitHub repo and tutorial page as part of the paper. It has the code base to replicate the type of analysis using a smaller scale simulated data. The original data had more than 1.5 million responses gathered from more than 275,000 students. The simulated data mimics the sparse data structure in a smaller scale for easier replication of the analysis.
GitHub repo: https://github.com/czopluoglu/Duolingo_paper