Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing multidimensional IRT methods, one requires a factorization of the test items. For this task, linear exploratory factor analysis is used, making IRT a posthoc model. We propose skipping the initial factor analysis by using a sparsity-promoting horseshoe prior to perform factorization directly within the IRT model so that all training occurs in a single self-consistent step. Being a hierarchical Bayesian model, we adapt the WAIC to the problem of dimensionality selection. IRT models are analogous to probabilistic autoencoders. By binding the generative IRT model to a Bayesian neural network (forming a probabilistic autoencoder), one obtains a scoring algorithm consistent with the interpretable Bayesian model. In some IRT applications the black-box nature of a neural network scoring machine is desirable. In this manuscript, we demonstrate within-IRT factorization and comment on scoring approaches.
翻译:项目响应理论( IRT) 是一个非线性基因化的遗传性概率模型, 用于使用考试来识别、 量化和比较个人( 相对于同龄人) 在感兴趣的人群中的潜在特征。 在先前存在的多维的 IRT 方法中, 需要一个测试项目的因子化。 对于此任务, 使用线性探索系数分析, 使 IRT 成为一个后热模型。 我们建议跳过初始要素分析, 在直接在 IRT 模型中进行分解之前, 使用 sparity- promoting horpshoe 来直接进行分解。 这样, 所有培训都以单一的自我一致步骤进行。 作为一种等级的 Bayesian 模型, 我们使 WAIC 适应于维度选择的问题。 IRT 模型类似于概率性自动电算器 。 通过将 IMT 模型连接到 Bayesian 神经网络( 形成一种可解释的自动电算模型), 我们建议跳式算算法与可解释的 Bayesian 模型一致。 在 IRT 应用神经网络评分数机器的黑箱性质时, 我们定了 。