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

我开发、编程和评估创新的潜变量模型。这项工作在社会科学/健康科学领域有广泛的应用，但主要的挑战在统计学(主要是NSERC主题MS28)。例如，大规模/操作测试跨越多个学科(教育、健康、执照、心理学)，并经常利用项目反应理论(IRT)。IRT提供了统计工具来估计项目的属性，构建测试，并对单个受访者进行评分。这种分数通常用于政策或高风险的决策。在这种情况下，心理测量模型必须满足一个或多个需求：1)多组估计和计划的缺失数据设计；2)长测试和许多受访者的快速估计；3)计算机自适应测试(CAT)的可行性；以及4)利益相关者的可解释性。*此类应用越来越多地使用多维IRT(MIRT)，它允许测量多个实质性结构。虽然有几种半参数和非参数IRT模型，但可以说没有一种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，许多一维半参数/非参数方法需要更多的研究来提高估计速度，或者使用多组、缺失数据和CAT。*建模能力的差距是关键，因为使用限制性参数模型或忽略多维可能导致对项目属性和个人分数的较差估计。因此，本文提出的研究计划的长期目标是将MIRT和半/非参数模型相结合，以开发出满足上述要求的新模型。*未来五年，我将把我在单调多项式(MP)模型方面的工作扩展到MIRT的情况。我认为，基于MP的模型具有解释优势，可以使用最大边际似然来估计，以促进多组和缺失数据。要实现以下短期目标，还需要做更多的工作：*1.新的基于MP的MIRT模型的开发和估计。*2.通过使用元启发式优化提高基于MP的模型的估计速度。*3.用于计算机自适应测试的基于MP的模型的开发和测试。*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，并且可能是对现有MIRT能力的开创性补充。这样的模型可以增强我们对半/非参数方法和元启发式的总体知识，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.