Observed Correlations between Person-means Depend on Within-person Correlations

Intensive longitudinal data have become a common data type across psychological disciplines. A key issue in the analysis of such data is the separation of within-person and between-person effects. This problem is well studied for the effect of between-person effects (e.g., varying intercepts) on within-person parameters (e.g., cross-lagged effects). In this paper, we discuss a less appreciated effect of within-person correlations on correlations between person-wise means. Using simulations and an analytical derivation, we show how observed correlations between person-wise means are a function of both population between-person correlations and within-person correlations. This has implications for the interpretation of statistical relationships between person-wise means, for example when estimated directly from the data or within stepwise approaches to estimating multilevel vector autoregressive models, such as in the popular R package mlVAR. We discuss implications for applied research and possible strategies to avoid this problem.