Estimating Both Directed and Undirected Contemporaneous Relations in Time Series Data Using Hybrid-Group Iterative Multiple Model Estimation

Researchers across varied fields increasingly are collecting and analyzing intensive longitudinal data (ILD) to examine processes across time at the individual level. Two types of relations are typically examined: lagged and contemporaneous. Lagged relations capture how variables at a prior time point can be used to explain variance in variables at a later time point. These are always modeled using auto- and cross-regressions by means of vector autoregression (VAR). By contrast, there are two types of relations commonly used to model the contemporaneous relations, which model how variables relate instantaneously. Until now, researchers must opt to either model contemporaneous relations as undirected relations among residuals (e.g., partial or full correlations) or as directed relations among the variables (e.g., paths or regressions). The choice for how to model contemporaneous relations has implications for inferences as well as the potential to introduce bias in the VAR lagged relations if the wrong type of relation is used. This article introduces a novel data-driven method, hybrid-group iterative multiple model estimation (GIMME), that provides a solution to the problem of having to choose one or the other type of contemporaneous relation to model. The modeling framework utilized in hybrid-GIMME allows for both types of contemporaneous relations in addition to the standard VAR relations. Both simulated and empirical data were used to test the performance of hybrid-GIMME. Results suggest this is a robust method for recovering contemporaneous relations in an exploratory manner, particularly with an ample number of time points per person. Translational Abstract This paper describes the development of a new statistical method for examining processes for individuals across time. There are two main types of contemporaneous relations: directed and undirected. A directed relation is typically interpreted as one variable (e.g., sleep quality) explains variability (or changes) in another variable (e.g., mood next day), while an undirected relation is commonly understood as two variables' variability being explained by a third one (e.g., mood the day before). Unlike most existing statistical methods that only allow for one of these two types of contemporaneous relations to be estimated, this new algorithm (hybrid-GIMME) allows for them both to be estimated simultaneously. And it thus allows for new questions to be explored. Both our simulation and empirical examples show promising results of this new method.

Automated summary

Researchers are increasingly using IL data to study individual-level processes, and the choice of how to model contemporaneous relations has implications for inferences and the potential introduction of bias in VAR lagged relations. This article introduces a novel data-driven method called GIMME that allows for modeling both types of contemporaneous relations and standard VAR relations simultaneously.