Dipartimento di Economia, Università di Perugia, Via A. Pascoli 20, 06123 , Perugia, Italy.
Dipartimento di Sanità Pubblica e Malattie Infettive, Sapienza - Università di Roma, Piazzale Aldo Moro, 5, 00186, Rome, Italy.
Psychometrika. 2017 Dec;82(4):952-978. doi: 10.1007/s11336-017-9576-7. Epub 2017 Sep 12.
We propose a nonparametric item response theory model for dichotomously-scored items in a Bayesian framework. The model is based on a latent class (LC) formulation, and it is multidimensional, with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class. Moreover, an innovative system of prior distributions is proposed following the encompassing approach, in which the largest model is the unconstrained LC model. A reversible-jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model. By suitably post-processing its output, we then make inference on the number of dimensions (i.e., number of groups of items measuring the same latent trait) and we cluster items according to the dimensions when unidimensionality is violated. The approach is illustrated by two examples on simulated data and two applications based on educational and quality-of-life data.
我们提出了一种贝叶斯框架下用于二分评分项目的非参数项目反应理论模型。该模型基于潜在类别（LC）公式，具有多维性，维度对应于基于条件成功概率之间的不等式约束在潜在类别上指定的同质组中项目的分区。此外，还提出了一种基于包容方法的创新先验分布系统，其中最大模型是无约束 LC 模型。描述了一种用于从包容模型的模型参数联合后验分布中进行抽样的可逆跳跃型算法。通过适当处理其输出，我们可以对维度数（即测量相同潜在特征的项目组的数量）进行推断，并在违反单维性时根据维度对项目进行聚类。该方法通过两个基于模拟数据的示例和两个基于教育和生活质量数据的应用进行了说明。
