Max Planck Institute for Human Development, Berlin, Germany.
Psychol Methods. 2012 Jun;17(2):176-92. doi: 10.1037/a0027543. Epub 2012 Apr 9.
Panel studies, in which the same subjects are repeatedly observed at multiple time points, are among the most popular longitudinal designs in psychology. Meanwhile, there exists a wide range of different methods to analyze such data, with autoregressive and cross-lagged models being 2 of the most well known representatives. Unfortunately, in these models time is only considered implicitly, making it difficult to account for unequally spaced measurement occasions or to compare parameter estimates across studies that are based on different time intervals. Stochastic differential equations offer a solution to this problem by relating the discrete time model to its underlying model in continuous time. It is the goal of the present article to introduce this approach to a broader psychological audience. A step-by-step review of the relationship between discrete and continuous time modeling is provided, and we demonstrate how continuous time parameters can be obtained via structural equation modeling. An empirical example on the relationship between authoritarianism and anomia is used to illustrate the approach.
面板研究是心理学中最受欢迎的纵向设计之一，它在多个时间点重复观察相同的对象。同时，也存在着广泛的不同方法来分析这些数据，自回归和交叉滞后模型是其中最著名的两种。不幸的是，在这些模型中，时间只是被隐含地考虑，因此很难考虑到不等间隔的测量时刻，或者比较基于不同时间间隔的研究中的参数估计。随机微分方程通过将离散时间模型与其在连续时间中的基础模型联系起来，为这个问题提供了一个解决方案。本文的目的是向更广泛的心理学受众介绍这种方法。提供了一个从离散时间建模到连续时间建模的关系的逐步回顾，我们展示了如何通过结构方程建模来获得连续时间参数。一个关于威权主义和失范之间关系的实证例子被用来举例说明这种方法。
