Department of Psychology, Arizona State University, PO Box 871104, Tempe, AZ, 85287, USA.
Centre for Educational Measurement, University of Oslo, Oslo, Norway.
Behav Res Methods. 2018 Aug;50(4):1398-1414. doi: 10.3758/s13428-017-0976-5.
In psychology, mixed-effects models and latent-curve models are both widely used to explore growth over time. Despite this widespread popularity, some confusion remains regarding the overlap of these different approaches. Recent articles have shown that the two modeling frameworks are mathematically equivalent in many cases, which is often interpreted to mean that one's choice of modeling framework is merely a matter of personal preference. However, some important differences in estimation and specification can lead to the models producing very different results when implemented in software. Thus, mathematical equivalence does not necessarily equate to practical equivalence in all cases. In this article, we discuss these two common approaches to growth modeling and highlight contexts in which the choice of the modeling framework (and, consequently, the software) can directly impact the model estimates, or in which certain analyses can be facilitated in one framework over the other. We show that, unless the data are pristine, with a large sample size, linear or polynomial growth, and no missing data, and unless the participants have the same number of measurements collected at the same set of time points, one framework is often more advantageous to adopt. We provide several empirical examples to illustrate these situations, as well as ample software code so that researchers can make informed decisions regarding which framework will be the most beneficial and most straightforward for their research interests.
在心理学中，混合效应模型和潜在曲线模型都被广泛用于探索随时间的增长。尽管这些方法非常受欢迎，但在这些不同方法的重叠方面仍存在一些混淆。最近的一些文章表明，这两种建模框架在许多情况下在数学上是等效的，这通常被解释为模型框架的选择仅仅是个人偏好的问题。然而，在估计和规范方面的一些重要差异可能导致模型在软件中产生非常不同的结果。因此，数学等效性并不一定在所有情况下都等同于实际等效性。在本文中，我们将讨论这两种常见的增长建模方法，并强调在哪些情况下选择建模框架（因此选择软件）会直接影响模型估计，或者在哪些情况下，一个框架比另一个框架更适合进行某些分析。我们表明，除非数据是原始的，具有较大的样本量、线性或多项式增长且没有缺失数据，并且除非参与者在相同的一组时间点收集相同数量的测量值，否则通常采用一个框架更有利。我们提供了几个实证示例来说明这些情况，并提供了大量的软件代码，以便研究人员能够就最有利于和最直接适用于其研究兴趣的框架做出明智的决策。
