Flexible Bayesian modelling in dichotomous item response theory using mixtures of skewed item curves

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2022-07-05 DOI:10.1111/bmsp.12282
Flávio B. Gonçalves, Juliane Venturelli S. L., Rosangela H. Loschi
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引用次数: 0

Abstract

Most item response theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals taking a test. This assumption restricts the use of those models to the case in which all items behave symmetrically. On the other hand, asymmetric models proposed in the literature impose that all the items in a test behave asymmetrically. This assumption is inappropriate for great majority of tests which are, in general, composed of both symmetric and asymmetric items. Furthermore, a straightforward extension of the existing models in the literature would require a prior selection of the items' symmetry/asymmetry status. This paper proposes a Bayesian IRT model that accounts for symmetric and asymmetric items in a flexible but parsimonious way. That is achieved by assigning a finite mixture prior to the skewness parameter, with one of the mixture components being a point mass at zero. This allows for analyses under both model selection and model averaging approaches. Asymmetric item curves are designed through the centred skew normal distribution, which has a particularly appealing parametrization in terms of parameter interpretation and computational efficiency. An efficient Markov chain Monte Carlo algorithm is proposed to perform Bayesian inference and its performance is investigated in some simulated examples. Finally, the proposed methodology is applied to a data set from a large-scale educational exam in Brazil.

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基于混合倾斜项目曲线的二分类项目反应理论中的灵活贝叶斯建模
大多数项目反应理论(IRT)的二分类反应模型都是基于probit或logit链接函数,这些函数假设答对的概率与被试个体的潜在特征之间存在对称关系。这个假设限制了这些模型的使用,在这种情况下,所有项目的行为都是对称的。另一方面,文献中提出的非对称模型要求测试中的所有项目都表现得不对称。这种假设不适用于绝大多数测试,这些测试通常由对称和非对称项目组成。此外,文献中现有模型的直接扩展将需要事先选择项目的对称/不对称状态。本文提出了一个贝叶斯IRT模型,该模型以一种灵活而简洁的方式考虑了对称和非对称项目。这是通过在偏度参数之前分配一个有限混合来实现的,其中一个混合分量是零点质量。这允许在模型选择和模型平均方法下进行分析。非对称项目曲线通过中心偏态正态分布设计,在参数解释和计算效率方面具有特别吸引人的参数化。提出了一种高效的马尔可夫链蒙特卡罗算法来进行贝叶斯推理,并通过一些仿真实例对其性能进行了研究。最后,将提出的方法应用于巴西大规模教育考试的数据集。
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来源期刊
CiteScore
5.00
自引率
3.80%
发文量
34
审稿时长
>12 weeks
期刊介绍: The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.
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