Ferrando Pere J, Navarro-González David
"Rovira i Virgili" University, Tarragona, Spain.
Educ Psychol Meas. 2021 Dec;81(6):1029-1053. doi: 10.1177/0013164421998412. Epub 2021 Mar 10.
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“对偶”模型（DMs）将项目和个体都视为差异测量误差的来源，到目前为止仅针对单维测量提出。本文提出了现有DMs的两种多维扩展：M-DTCRM（对偶瑟斯顿连续反应模型），用于（近似）连续反应；M-DTGRM（对偶瑟斯顿等级反应模型），用于有序分类反应（包括二元反应）。首先提出并讨论了基于多维位置指数概念扩展到多内容维度情况的基本原理。然后，使用因子分析和项目反应理论参数化来描述模型。最后讨论了（a）校准项目、（b）对个体评分、（c）评估模型适用性和（d）评估测量精度的程序。模拟结果表明该提议相当可行，还提供了一个基于人格数据的示例。对于多维问卷的情况，这些提议尤其有意义，因为如果在单独量表基础上拟合现有的单维DMs，每个量表的项目数量将不足以得出稳定的估计值。
