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.

翻译：工作能力失能评估量表（WD-FAB）是一种基于项目反应理论（IRT）的多维测量工具，旨在根据项目库的响应评估与工作相关的心理和身体功能。在之前的迭代中，该量表采用传统方式开发——通过线性分解和原假设统计检验进行项目划分/选择，最后对不相交的单维IRT模型进行事后校准。因此，与许多其他IRT测量工具一样，WD-FAB是一种事后模型。其基于探索性因子分析的项目划分忽略最终的非线性IRT模型，且未以与最终模型拟合优度一致的方式进行。本文开发了一种贝叶斯层次模型，用于自洽地执行以下同步任务：量表分解、项目选择、参数识别和响应评分。该方法基于稀疏性收缩避免了开发多维IRT模型通常所需的线性分解和原假设统计检验，从而使项目划分与最终的非线性因子模型一致。我们还将多维IRT模型类比为概率自编码器，利用编码器函数将能力参数的推理从项目响应中摊销出来。该编码器函数等价于随机变分贝叶斯期望最大化（VBEM）过程中的“VBE”步骤，用于对整个模型进行近似贝叶斯推断。我们以WD-FAB项目响应样本为例应用该方法，并将所得项目区分度与传统事后方法的结果进行比较。