A State Space Modeling Approach to Mediation Analysis

Abstract

Mediation is a causal process that evolves over time. Thus, a study of mediation requires data collected throughout the process. However, most applications of mediation analysis use cross-sectional rather than longitudinal data. Another implicit assumption commonly made in longitudinal designs for mediation analysis is that the same mediation process universally applies to all members of the population under investigation. This assumption ignores the important issue of ergodicity before aggregating the data across subjects. We first argue that there exists a discrepancy between the concept of mediation and the research designs that are typically used to investigate it. Second, based on the concept of ergodicity, we argue that a given mediation process probably is not equally valid for all individuals in a population. Therefore, the purpose of this article is to propose a two-faceted solution. The first facet of the solution is that we advocate a single-subject time-series design that aligns data collection with researchers’ conceptual understanding of mediation. The second facet is to introduce a flexible statistical method—the state space model—as an ideal technique to analyze single-subject time series data in mediation studies. We provide an overview of the state space method and illustrative applications using both simulated and real time series data. Finally, we discuss additional issues related to research design and modeling.

When Time Makes a Difference: Addressing Ergodicity and Complexity in Education

“…Another approach to obtaining a better understanding of the impact of exogenous processes on daily high school attendance is a mediation analysis in which daily attendance would conceptualized as an outcome trajectory, which is linked to a trajectory describing an exogenous process, allowing a direct attribution of shifts in the behavior of one to the behavior of the other. More detailed discussions of this approach can be found in Gu, Preacher and Ferrer (2014), Molenaar et al (2009), Vallacher and Novak (2009), and Wong, Vallacher and Novak (2014).…”

“…A related point is that conventional scholarship in education prefers to study exogenous causal processes rather than endogenous ones, which is to say that, for example, the impact of intervention x on behavior y is examined, without taking a detailed look at behavior y at previous occasions to assess y's impact on itself at a later date (van Geert, 2009). The focus on exogenous processes across individuals presupposes that hypothesized causal mechanisms that are confirmed based on group means are in alignment with the causal mechanism governing the behavior of each of the individual cases within that group (Gu, Preacher, & Ferrer, 2014). Verification of this assumption is of practical value because it qualifies the conclusions that are drawn from the statistical association between group means and it draws attention to the particularities of the individual case.…”

Viii. The Past, Present, and Future of Developmental Methodology

“…The transition matrix reflects the effect that the current state vector has on a predicted future state vector. The state space modeling framework has been expanded to have applications in mediation analysis (Gu, Preacher, & Ferrer, 2014), multilevel regression models, and multilevel confirmatory factor models (Gu, Preacher, Wu, & Yung, 2014).…”

Illustrating idiographic methods for translation research: moderation effects, natural clinical experiments, and complex treatment-by-subgroup interactions

“…Yet, alternative statistics may be more appropriate, offer greater power (in the case of LR χ 2 ), or provide requisite conservative adjustments of which the field is not yet aware. Some recent advances in idiographic statistics include a bootstrapping technique for modeling mediation analysis using time series data [14], power analysis for randomized ordering of competing ORIGINAL RESEARCH treatments [15], and using "moving windows" methods and non-parametric statistical testing to identify distinct within-person patterns of behavior to forecast a person's change from one pattern to another [16].…”