A Multidimensional Finite Mixture Structural Equation Model for Nonignorable Missing Responses to Test Items
A Multidimensional Finite Mixture Structural Equation Model for Nonignorable Missing Responses to Test Items
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DOI：
10.1080/10705511.2014.937376
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发表时间：
2015-07-03
影响因子：
6
通讯作者：
Bartolucci, Francesco
中科院分区：
文献类型：
--
作者：
Bacci, Silvia;Bartolucci, Francesco
本文提出了一个结构方程模型，它简化为一个多维潜在类别项目反应理论模型，用于分析具有不可重复缺失的二进制项目反应。缺失机制由2组潜在变量驱动：一组描述响应倾向，另一组涉及测试项目测量的能力。假设这些潜在变量具有离散分布，以减少关于模型潜在结构的参数假设的数量。个体协变量也可以通过潜变量分布的多项式逻辑参数化来纳入。由于这种分布的离散性，该模型是有效地估计的期望最大化算法。模拟研究进行评估的参数估计的有限样本性质。此外，一个应用程序说明了来自学生入学考试的数据，录取到一些大学课程。
We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with nonignorable missingness. The missingness mechanism is driven by 2 sets of latent variables: one describing the propensity to respond and the other referred to the abilities measured by the test items. These latent variables are assumed to have a discrete distribution, so as to reduce the number of parametric assumptions regarding the latent structure of the model. Individual covariates can also be included through a multinomial logistic parameterization for the distribution of the latent variables. Given the discrete nature of this distribution, the proposed model is efficiently estimated by the expectation-maximization algorithm. A simulation study is performed to evaluate the finite-sample properties of the parameter estimates. Moreover, an application is illustrated with data coming from a student entry test for the admission to some university courses.