The interpretation of cross-effects from vector autoregressive models to infer structure and causality among constructs is widespread and sometimes problematic. I describe problems in the interpretation of cross-effects when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps (as in e.g., structural equation modeling)-zeroes in a discrete-time temporal matrix do not necessarily correspond to zero effects in the underlying continuous processes, and vice versa. This has implications for the common case when the presence or absence of cross-effects is used for inference about underlying causal processes. I demonstrate these problems via simulation, and also show that when an underlying set of processes are continuous in time, even relatively few direct causal links can result in much denser temporal effect matrices in discrete-time. I demonstrate one solution to these issues, namely parameterizing the system as a stochastic differential equation and focusing inference on the continuous-time temporal effects. I follow this with some discussion of issues regarding the switch to continuous-time, specifically regularization, appropriate measurement time lag, and model order. An empirical example using intensive longitudinal data highlights some of the complexities of applying such approaches to real data, particularly with respect to model specification, examining misspecification, and parameter interpretation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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具有交叉滞后效应的推理-时间问题。


对向量自回归模型的交叉效应进行解释以推断构造之间的结构和因果关系是普遍存在的，但有时存在问题。我描述了交叉效应解释中的问题，当被认为随时间连续波动的过程被建模为仅在离散步骤中变化时（如结构方程建模）——离散时间中的零时间矩阵不一定对应于底层连续过程中的零效应，反之亦然。当交叉效应的存在或不存在用于推断潜在因果过程时，这对常见情况有影响。我通过模拟演示了这些问题，并且还表明，当一组基础过程在时间上连续时，即使相对较少的直接因果关系也可以在离散时间中产生更密集的时间效应矩阵。我演示了这些问题的一种解决方案，即将系统参数化为随机微分方程，并将推理重点放在连续时间的时间效应上。接下来，我讨论了有关切换到连续时间的问题，特别是正则化、适当的测量时滞和模型顺序。使用密集纵向数据的实证示例强调了将此类方法应用于实际数据的一些复杂性，特别是在模型规范、检查错误规范和参数解释方面。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。