arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.10352stat.ME
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因果效应下单波因子分析的维数不确定性

On the dimensional indeterminacy of one-wave factor analysis under causal effects

Tyler J. VanderWeele, Charles J. K. Batty

摘要:

它示出,与两套指标,分别加载在两个不同的因素,独立于另一个条件的过去,如果是这样的情况下,至少一个因素的因果关系影响其他的,那么,在许多设置中,该过程将收敛到一个因素模型,其中一个单一的因素将足以捕捉指标之间的协方差结构。使用一波数据的因子分析无法区分具有单个因子的因子模型与具有两个因果相关因子的因子模型。因此,除非可以先验地排除因素之间的因果关系,否则对单个因素进行单波因素分析的所谓经验证据仍然存在单个因素或两个因素相互因果影响的可能性。解释心理量表的因素结构,如焦虑和抑郁的自我报告量表,或幸福和目的的影响,进行了讨论。通过模拟进一步说明了结果,以深入了解在更现实的设置之前的收敛过程的结果的实际影响。一些进一步的概括任意数量的基本因素指出。

英文摘要:

It is shown, with two sets of indicators that separately load on two distinct factors, independent of one another conditional on the past, that if it is the case that at least one of the factors causally affects the other, then, in many settings, the process will converge to a factor model in which a single factor will suffice to capture the covariance structure among the indicators. Factor analysis with one wave of data can then not distinguish between factor models with a single factor versus those with two factors that are causally related. Therefore, unless causal relations between factors can be ruled out a priori, alleged empirical evidence from one-wave factor analysis for a single factor still leaves open the possibilities of a single factor or of two factors that causally affect one another. The implications for interpreting the factor structure of psychological scales, such as self-report scales for anxiety and depression, or for happiness and purpose, are discussed. The results are further illustrated through simulations to gain insight into the practical implications of the results in more realistic settings prior to the convergence of the processes. Some further generalizations to an arbitrary number of underlying factors are noted.

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