multi-level modeling
Definition
Multi-level modeling refers to a class of statistical approaches designed to separate within-person and between-person sources of variance in intensive longitudinal data, where multiple subjects are each measured repeatedly over time. A common implementation involves multilevel vector autoregressive models, in which person-wise sample means serve as proxies for true stable means, allowing researchers to estimate both temporal within-person dynamics and between-person correlations among stable traits. However, person-wise sample means are not purely reflective of between-person variance because they absorb within-person deviations, meaning the variance-covariance structure of those means is partially determined by within-person correlations. This contamination can produce spurious between-person correlations even when no true population-level association exists, with the bias growing most severe when the number of time points per person is low and within-person effects are strong. Approaches that jointly estimate within- and between-person effects in a single step are recommended to avoid this problem.
Sources: Haslbeck & Epskamp (2024)
Related Terms
- longitudinal data analysis (1 shared article)
- vector autoregressive models (1 shared article)
- separating within- and between-person effects (1 shared article)
Applications
Multi-level Modeling and Within-person Correlation
Within-person correlations systematically bias between-person parameter estimates when multi-level modeling relies on person-wise sample means as proxies for true stable means. Simulations using a multilevel lag-1 vector autoregressive model demonstrate that a correlation between person-wise means can be observed even when the data-generating mechanism includes no between-person correlation whatsoever, because the sample means absorb within-person variance. The magnitude of this bias depends on the ratio of between-person to within-person variance and on how many time points are available per person.
Sources: Haslbeck & Epskamp (2024)
Multi-level Modeling and Between-person Correlation
Between-person correlations, defined as associations among the stable person-specific means, are the target of inference in multi-level modeling when researchers wish to study trait-level relationships. Estimating these correlations from person-wise sample means yields biased estimates because those means conflate the true stable component with time-varying within-person deviations.
Sources: Haslbeck & Epskamp (2024)
