# Autoencoded sparse Bayesian in-IRT factorization, calibration, and amortized inference for the Work Disability Functional Assessment Battery

arXiv: https://arxiv.org/abs/2210.10952 · HTML: https://mlsanity.com/paper/2210.10952/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Understanding predictive information criteria for Bayesian models](https://mlsanity.com/paper/1307.5928/) (2013)
- [Sparsity information and regularization in the horseshoe and other shrinkage priors](https://mlsanity.com/paper/1707.01694/) (2017)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Designing Inherently Interpretable Machine Learning Models](https://mlsanity.com/paper/2111.01743/) (2021)
- [Lasso Meets Horseshoe : A Survey](https://mlsanity.com/paper/1706.10179/) (2017)
- [On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior](https://mlsanity.com/paper/1610.05559/) (2016)
- [Hyperprior Induced Unsupervised Disentanglement of Latent Representations](https://mlsanity.com/paper/1809.04497/) (2018)
- [Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization](https://mlsanity.com/paper/2012.04171/) (2020)
- [Interpretable VAEs for nonlinear group factor analysis](https://mlsanity.com/paper/1802.06765/) (2018)
- [Predictive Bayesian selection of multistep Markov chains, applied to the detection of the hot hand and other statistical dependencies in free throws](https://mlsanity.com/paper/1706.08881/) (2017)
- [Probabilistically-autoencoded horseshoe-disentangled multidomain item-response theory models](https://mlsanity.com/paper/1912.02351/) (2019)
- [Regularized Bayesian calibration and scoring of the WD-FAB IRT model improves predictive performance over marginal maximum likelihood](https://mlsanity.com/paper/2010.01396/) (2020)

## Abstract (arXiv)

The Work Disability Functional Assessment Battery (WD-FAB) is a multidimensional item response theory (IRT) instrument designed for assessing work-related mental and physical function based on responses to an item bank. In prior iterations it was developed using traditional means -- linear factorization and null hypothesis statistical testing for item partitioning/selection, and finally, posthoc calibration of disjoint unidimensional IRT models. As a result, the WD-FAB, like many other IRT instruments, is a posthoc model. Its item partitioning, based on exploratory factor analysis, is blind to the final nonlinear IRT model and is not performed in a manner consistent with goodness of fit to the final model. In this manuscript, we develop a Bayesian hierarchical model for self-consistently performing the following simultaneous tasks: scale factorization, item selection, parameter identification, and response scoring. This method uses sparsity-based shrinkage to obviate the linear factorization and null hypothesis statistical tests that are usually required for developing multidimensional IRT models, so that item partitioning is consistent with the ultimate nonlinear factor model. We also analogize our multidimensional IRT model to probabilistic autoencoders, specifying an encoder function that amortizes the inference of ability parameters from item responses. The encoder function is equivalent to the "VBE" step in a stochastic variational Bayesian expectation maximization (VBEM) procedure that we use for approxiamte Bayesian inference on the entire model. We use the method on a sample of WD-FAB item responses and compare the resulting item discriminations to those obtained using the traditional posthoc method.