Three-level vector autoregressive models

The growing use of intensive longitudinal studies has heightened demand for advanced modeling approaches to better understand temporal dynamics of individual change. Although widely used multilevel vector autoregressive models can capture both intraindividual dynamics and interindividual differences, current implementations are restricted to two-level analyses. This can be problematic, as three-level nested structures are common in practice-for instance, individuals may be further clustered within higher level units, or weekday assessments are nested within weeks that are further nested within individuals. Existing two-level frameworks cannot adequately model such hierarchies, potentially leading to incorrect estimation and inferences about intraindividual dynamics. To address this issue, we introduce a three-level vector autoregressive modeling framework and provide corresponding Bayesian estimation algorithms. We evaluate the estimation performance of three key model specifications-unconditional univariate, conditional univariate (with Level 2 and Level 3 covariates), and unconditional bivariate-through a set of simulation studies. By varying sample sizes at all three levels and key population parameters, these simulations offer initial evidence on how sample sizes across levels influence model performance. An empirical example using ratings of children's daily emotional states during their first kindergarten month illustrates the three-level vector autoregressive framework's utility. We conclude by summarizing key findings, offering practical guidance for application, and pointing out limitations and future directions. (PsycInfo Database Record (c) 2026 APA, all rights reserved).