Estimating correlations in low-reliability settings with constrained hierarchical models.

IF 4.6 2区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL
Mahbod Mehrvarz, Jeffrey N Rouder
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引用次数: 0

Abstract

It is popular to study individual differences in cognition with experimental tasks, and the main goal of such approaches is to analyze the pattern of correlations across a battery of tasks and measures. One difficulty is that experimental tasks are often low in reliability as effects are small relative to trial-by-trial variability. Consequently, it remains difficult to accurately estimate correlations. One approach that seems attractive is hierarchical modeling where trial-by-trial variability and variability across conditions, tasks, and individuals are modeled separately. Here we show that hierarchical models may reduce the error in estimating correlations up to 43%, but only if substantive constraint is imposed. The approach here is Bayesian, and we develop novel Bayesian hierarchical factor models for experiments where trials are nested in conditions, tasks, and individuals. The prior on covariances across tasks can either be unconstrained, in which there is little error reduction, or constrained, in which there is substantial error reduction. The constraints are: (1) There is a low-dimension factor structure underlying the covariation across tasks, and (2) all loadings are non-negative leading to a positive manifold on correlations. We argue that both of these assumptions are reasonable in cognitive domains, and that with them, researchers may profitably use hierarchical models to estimate correlations across tasks in low-reliability settings.

用约束层次模型估计低可靠性设置中的相关性。
用实验任务来研究认知的个体差异是很流行的,这种方法的主要目标是分析一系列任务和测量之间的相关性模式。一个困难是,实验任务的可靠性通常很低,因为相对于每个试验的可变性,效果很小。因此,仍然很难准确地估计相关性。一种看起来很有吸引力的方法是分层建模,其中逐个试验的可变性和跨条件、任务和个人的可变性分别建模。在这里,我们表明,层次模型可以减少估计相关性的误差高达43%,但只有在施加实质性约束的情况下。这里的方法是贝叶斯,我们为实验开发了新的贝叶斯分层因素模型,其中试验嵌套在条件,任务和个人中。跨任务协方差的先验可以是无约束的,在这种情况下几乎没有减少误差,也可以是有约束的,在这种情况下有很大的减少误差。约束条件为:(1)任务间协变存在低维因子结构,(2)所有负载都是非负的,导致相关性呈正流形。我们认为这两种假设在认知领域都是合理的,并且有了它们,研究人员可以有效地使用分层模型来估计低可靠性设置下任务之间的相关性。
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来源期刊
CiteScore
10.30
自引率
9.30%
发文量
266
期刊介绍: Behavior Research Methods publishes articles concerned with the methods, techniques, and instrumentation of research in experimental psychology. The journal focuses particularly on the use of computer technology in psychological research. An annual special issue is devoted to this field.
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