Item response theory “dual” models (DMs) in which both items and individuals are viewed as sources of differential measurement error so far have been proposed only for unidimensional measures. This article proposes two multidimensional extensions of existing DMs: the M-DTCRM (dual Thurstonian continuous response model), intended for (approximately) continuous responses, and the M-DTGRM (dual Thurstonian graded response model), intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the item response theory parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The simulation results suggest that the proposal is quite feasible, and an illustrative example based on personality data is also provided. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates if the existing unidimensional DMs were fitted on a separate-scale basis.

项目反应理论“双重”模型 (DMs)，其中项目和个人都被视为差异测量误差的来源，迄今为止仅被提出用于一维测量。本文提出了现有 DM 的两个多维扩展：M-DTCRM（双 Thurstonian 连续响应模型），用于（近似）连续响应，以及 M-DTGRM（双 Thurstonian 分级响应模型），用于有序分类响应（包括二进制）。首先提出并讨论了基于多维位置索引概念的多内容维度情况扩展的基本原理。然后，使用因子分析和项目响应理论参数化来描述模型。(a) 校准项目，(b) 给个人评分的程序，(c) 评估模型适当性，和 (d) 评估测量精度。模拟结果表明该提议是非常可行的，并且还提供了基于个性数据的说明性示例。提交的建议特别适用于多维问卷的情况，如果现有的单维 DM 是在单独的尺度基础上拟合的，那么每个尺度的项目数量不足以得出稳定的估计值。