  Item Response Theory (IRT) is a ubiquitous model for understanding human
behaviors and attitudes based on their responses to questions. Large modern
datasets offer opportunities to capture more nuances in human behavior,
potentially improving psychometric modeling leading to improved scientific
understanding and public policy. However, while larger datasets allow for more
flexible approaches, many contemporary algorithms for fitting IRT models may
also have massive computational demands that forbid real-world application. To
address this bottleneck, we introduce a variational Bayesian inference
algorithm for IRT, and show that it is fast and scalable without sacrificing
accuracy. Applying this method to five large-scale item response datasets from
cognitive science and education yields higher log likelihoods and higher
accuracy in imputing missing data than alternative inference algorithms. Using
this new inference approach we then generalize IRT with expressive Bayesian
models of responses, leveraging recent advances in deep learning to capture
nonlinear item characteristic curves (ICC) with neural networks. Using an
eigth-grade mathematics test from TIMSS, we show our nonlinear IRT models can
capture interesting asymmetric ICCs. The algorithm implementation is
open-source, and easily usable.
