Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Wan-Lun Wang, Luis M. Castro, Huei-Jyun Li, Tsung-I Lin
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引用次数: 0

Abstract

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of t $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

有删减反应和外部协变量的 t 因子分析器混合物:秘鲁教育数据的应用
分析教育测试的数据使政府能够为提高社会中个人的生活质量作出决定。统计学家的主要职责之一是开发模型,为决策者提供有关教育测试试图代表的潜在过程的相关信息。混合t $$ t $$因子分析器(MtFA)已经成为一种强大的设备,用于基于模型的聚类和高维数据的分类,这些数据包含一组或几组具有较宽尾部或异常异常值的观测值。本文考虑了MtFA的一个扩展,即MtFAC模型,通过合并外部协变量来实现截尾数据的鲁棒聚类。在MtFAC中包含协变量的灵活性增强,可以对因变量进行特定集群的多变量回归分析,这些因变量的响应由实验设备的上限和/或下限检测限引起。针对该模型的极大似然估计,提出了一种交替期望条件最大化(AECM)算法。通过两个仿真实验验证了所提技术的有效性。此外,所提出的方法应用于秘鲁2007年早期阅读评估的数据,从分析中获得的结果为秘鲁学生的阅读技能提供了新的见解。
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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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