One Does Not Simply Correct for Serial Dependence

Serial dependence is present in most time series data sets collected in psychological research. This paper investigates the implications of various approaches for handling such serial dependence, when one is interested in the linear effect of a time-varying covariate on the time-varying criterion. Specifically, the serial dependence is either neglected, corrected for by specifying autocorrelated residuals, or modeled by including a lagged version of the criterion as an additional predictor. Using both empirical and simulated data, we showcase that the obtained results depend considerably on which approach is selected. We discuss how these differences can be explained by understanding the restrictions imposed under the various approaches. Based on the insight that all three approaches are restricted versions of an autoregressive distributed lag model, we demonstrate that accessible statistical tools, such as information criteria and likelihood-ratio tests can be used to justify a chosen approach empirically.

心理学研究中采集的绝大多数时间序列数据集均存在序列相依性（serial dependence）现象。本文针对当研究者关注时变协变量对时变因变量的线性效应时，各类处理此类序列相依性的方法所产生的影响展开了探究。具体而言，研究者可选择忽略序列相依性、通过设定自相关残差进行校正，或是将因变量的滞后项作为额外预测变量纳入模型以对其进行建模。本文通过实证数据与模拟数据相结合的方式，证明所得研究结果会因所选方法的不同而产生显著差异。本文还探讨了如何通过理解各类方法所施加的约束条件，来解释这些结果差异。基于三类方法均为自回归分布滞后模型（autoregressive distributed lag model）的受限形式这一核心认知，本文证明了信息准则（information criteria）、似然比检验（likelihood-ratio tests）等易用的统计工具，可用于从实证层面验证所选方法的合理性。