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) 2025 APA, all rights reserved).

中文翻译：

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使用交叉滞后效应进行推理 - 时间问题。


对向量自回归模型的交叉效应的解释以推断结构之间的结构和因果关系是广泛的，有时是有问题的。我描述了当被认为在时间上连续波动的过程被建模为仅在离散步骤中变化时（如例如，结构方程建模）时，我描述了交叉效应解释中的问题——离散时间矩阵中的零不一定对应于潜在连续过程中的零效应，反之亦然。这对于使用存在或不存在交叉效应来推断潜在因果过程的常见情况具有影响。我通过仿真演示了这些问题，并且还表明，当一组潜在的过程在时间上是连续的时，即使是相对较少的直接因果关系也会导致离散时间中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、适当的测量时间滞后和模型顺序。使用密集纵向数据的经验示例突出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） 2025 APA，保留所有权利）。