vector autoregressive models
Definition
Vector autoregressive models are multivariate time-series models that estimate lagged relationships among a set of variables across discrete time points, commonly applied to intensive longitudinal data in psychology to separate within-person dynamics from stable between-person differences. In a multilevel formulation, the model incorporates person-specific means, person-specific lagged effects, and person-specific innovation variances, allowing researchers to characterize both temporal auto-regression and contemporaneous covariance structure for the average person. A central concern with stepwise estimation approaches, such as those implemented in the mlVAR R package, is that person-wise sample means used as proxies for true person-wise means carry contamination from within-person deviations, so that observed correlations between those means reflect a blend of true between-person correlations and within-person correlations rather than the former alone. This bias is most pronounced when the number of time points per person is low and between-person variance is small relative to within-person variance.
Sources: Haslbeck & Epskamp (2024)
Related Terms
- longitudinal data analysis (1 shared article)
- multi-level modeling (1 shared article)
- separating within- and between-person effects (1 shared article)
Applications
Vector Autoregressive Models and Within-person Correlations
Within-person correlations in a multilevel VAR framework directly distort estimates of between-person effects when person-wise sample means are used as proxies for true person-wise means. Simulation evidence shows that correlations between person-wise means can appear even when the data-generating mechanism includes no between-person correlation whatsoever, because the sample means are partly determined by within-person deviations. The variance-covariance structure of person-wise sample means is therefore a function of both population between-person correlations and within-person correlations, not of the former alone.
Sources: Haslbeck & Epskamp (2024)
Vector Autoregressive Models and Between-person Effects
Between-person effects in the VAR context are defined as the variance-covariance structure of the stable person-specific means, representing relationships among traits rather than day-to-day fluctuations. The mlVAR stepwise approach estimates these effects from correlations among person-wise sample means, but this strategy conflates true between-person relationships with artifacts introduced by within-person dynamics. Methods that jointly estimate within- and between-person effects in a single step are recommended to obtain unbiased between-person parameters.
Sources: Haslbeck & Epskamp (2024)
