Semi-parametric multidimensional item response models for large-scale and operational testing

我开发，编程和评估创新的潜在变量模型。这项工作在社会/健康科学中有广泛的应用，但主要的挑战是在统计方面（主要是NSERC主题MS28）。例如，大规模/操作性测试跨越多个学科（教育、卫生、执照、心理学），并且经常使用项目反应理论（IRT）。IRT提供了统计工具来估计项目的属性、构造测试和对个别应答者进行评分。这些分数通常用于政策或高风险决策。在这种情况下，心理测量模型通常必须满足一个或多个要求：1)多组估计和计划缺失数据设计；2)快速估计，测试时间长，受访者多；3)计算机适应性测试（CAT）的可行性；利益相关者的可解释性。这些应用程序越来越多地使用多维IRT (MIRT)，它允许测量多个实体结构。虽然有几种半参数和非参数IRT模型，但可以论证的是，没有一种MIRT方法既能放松典型的参数假设，又能满足上述要求。事实上，许多一维半/非参数方法需要更多的研究来提高估计速度，或用于多组、缺失数据和CAT。这种建模能力的差距是解决的关键，因为使用限制性参数模型或忽略多维度可能导致对项目属性和个人分数的估计不准确。因此，提出的研究计划的长期目标是将MIRT和半/非参数建模相结合，开发能够满足上述需求的新模型。在接下来的五年里，我将把我在单调多项式（MP）模型上的工作扩展到MIRT的情况。我认为基于mp的模型具有解释性优势，可以使用最大边际似然来估计多组和缺失数据。要实现下列短期目标，还需要做许多额外的工作：基于mp的新型MIRT模型的开发与估计。利用元启发式优化提高基于mp模型的估计速度。开发和测试用于计算机自适应测试的基于mp的模型。这项研究需要分析/技术工作（目标1和3）和统计计算（所有目标）。真实数据和蒙特卡罗模拟将比较新的基于mp的方法与现有的非参数和参数(M)IRT模型。由于缺乏替代方案，新的半参数MIRT模型是原创的，并且可能是对当前MIRT功能的突破性补充。这样的模型可以增强我们对半/非参数方法和元启发式的知识，提高大规模/操作测试的有效性，并将作为未来发展的基准。

I develop, program, and evaluate innovative latent variable models. This work has broad applications across the social/health sciences, yet the main challenges are in statistics (primarily NSERC topic MS28).As an example, large-scale/operational testing spans multiple disciplines (education, health, licensure, psychology) and often makes use of item response theory (IRT). IRT provides statistical tools to estimate the properties of items, construct tests, and score individual respondents. Such scores are often used for policy or high-stakes decisions.In this context, psychometric models must often meet one or more demands: 1) Estimation with multiple groups and planned missing data designs; 2) Fast estimation with a long test and many respondents; 3) Feasibility with a computer adaptive test (CAT); and 4) Interpretability by stakeholders.Such applications increasingly use multidimensional IRT (MIRT), which allows measurement of multiple substantive constructs. While there are several semiparametric and nonparametric IRT models, there are arguably no MIRT approaches that can both relax typical parametric assumptions and meet the above demands. In fact, many unidimensional semi/nonparametric approaches require more research to improve estimation speed, or use with multiple groups, missing data, and in a CAT.This gap in modeling capacity is critical to address because use of a restrictive parametric model or ignoring multidimensionality can lead to poor estimates of item properties and individuals' scores. Therefore, the long-term objective of the proposed research program is integrate MIRT and semi/nonparametric modeling to develop new models that can meet the above demands.Over the next five years, I will extend my work on monotonic polynomial (MP) models to the case of MIRT. I argue that MP-based models have interpretational advantages and can be estimated using maximum marginal likelihood to facilitate multiple groups and missing data. Much additional work is required to achieve the following short-term objectives:1. The development and estimation of new MP-based MIRT models.2. Enhancement of the estimation speed of MP-based models through use of metaheuristic optimization.3. Development and testing of MP-based models for use in computer adaptive testing.This research requires analytical/technical work (Objectives 1 and 3) and statistical computing (all Objectives). Real data and Monte Carlo simulations will compare new MP-based approaches versus extant nonparametric and parametric (M)IRT models.Given a lack of alternatives, new semiparametric MIRT models are original and a potentially groundbreaking addition to current MIRT capabilities. Such models can enhance our knowledge of semi/nonparametric approaches and metaheuristics in general, improve the validity of large-scale/operational tests, and will serve as a benchmark for future developments.