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

Intensive longitudinal data have become a common data type across psychological disciplines in the last decade. 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, such as varying intercepts, on within-person parameters, such as 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 personwise means are a function of both population between-person correlations and within-person correlations. This has implications for the interpretation of statistical relationships between personwise 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.