快速估计具有顺序、连续和计数观测变量的性能和过程数据的广义线性潜变量模型。

IF 1.5 3区 心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Maoxin Zhang, Björn Andersson, Shaobo Jin
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引用次数: 0

摘要

在心理和教育测量中经常会出现不同的数据类型,如记录表现和过程数据(如反应时间和操作次数)的基于计算机的评估。对这类数据建模需要针对每种数据类型建立特定的模型,并适应多个变量之间复杂的依赖关系。广义线性潜变量模型适用于同时对混合数据建模,但估算需要大量计算。快速的解决方案是使用拉普拉斯近似,但现有的混合数据类型联合建模方法仅限于序数和连续数据。为了解决这一局限性,我们推导出一种高效的估计方法,利用一阶或二阶拉普拉斯近似同时对序数数据、连续数据和计数数据建模。我们以实例说明了该方法,并进行了模拟,以评估该方法在估计效率、收敛性和参数恢复方面的性能。结果表明,与一阶拉普拉斯近似法相比,二阶拉普拉斯近似法能达到更高的收敛速度,并能产生准确而快速的参数估计,而时间成本会随着模型复杂度的提高而增加。此外,考虑同一刺激变量依赖性的模型比忽略依赖性的模型更符合经验数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables

Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables

Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.

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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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