Ariens Sigert, Adolf Janne K, Ceulemans Eva
Quantitative Psychology and Individual Differences, Faculty of Psychology and Educational Sciences, KU Leuven.
Multivariate Behav Res. 2023 Jul-Aug;58(4):687-705. doi: 10.1080/00273171.2022.2095247. Epub 2022 Aug 2.
First-order autoregressive models are popular to assess the temporal dynamics of a univariate process. Researchers often extend these models to include time-varying covariates, such as contextual factors, to investigate how they moderate processes' dynamics. We demonstrate that doing so has implications for how well one can estimate the autoregressive and covariate effects, as serial dependence in the variables can imply predictor collinearity. This is a noteworthy contribution, since in current practice serial dependence in a time-varying covariate is rarely considered important. We first recapitulate the role of predictor collinearity for estimation precision in an ordinary least squares context, by discussing how it affects estimator variances, covariances and correlations. We then derive a general formula detailing how predictor collinearity in first-order autoregressive models is impacted by serial dependence in the covariate. We provide a simulation study to illustrate the implications of the formula for different types of covariates. The simulation results highlight when the collinearity issue becomes severe enough to hamper interpretation of the effects. We also show that the effect estimates can be biased in small samples (i.e., 50 time points). Implications for study design, the use of time as a predictor, and related model variants are discussed.
一阶自回归模型常用于评估单变量过程的时间动态。研究人员经常扩展这些模型以纳入随时间变化的协变量，如情境因素，来研究它们如何调节过程的动态。我们证明，这样做会对估计自回归和协变量效应的效果产生影响，因为变量中的序列依赖性可能意味着预测变量的共线性。这是一个值得注意的贡献，因为在当前实践中，随时间变化的协变量中的序列依赖性很少被认为是重要的。我们首先通过讨论预测变量共线性如何影响估计量的方差、协方差和相关性，来概括其在普通最小二乘背景下对估计精度的作用。然后，我们推导了一个通用公式，详细说明一阶自回归模型中的预测变量共线性如何受到协变量中序列依赖性的影响。我们提供了一项模拟研究，以说明该公式对不同类型协变量的影响。模拟结果突出了共线性问题何时会严重到妨碍对效应的解释。我们还表明，在小样本（即50个时间点）中，效应估计可能存在偏差。文中讨论了对研究设计、将时间用作预测变量以及相关模型变体的影响。
