Considering between- and within-person relations in auto-regressive cross-lagged panel models for developmental data

Longitudinal data can provide inferences at both the between-person and within-person levels of analysis, but only to the extent that the statistical models chosen for data analysis are specified to adequately capture these distinct sources of association. The present work focuses on auto-regressive cross-lagged panel models, which have long been used to examine time-lagged reciprocal relations and mediation among multiple variables measured repeatedly over time. Unfortunately, many common implementations of these models fail to distinguish between-person associations among individual differences in the variables' amounts and changes over time, and thus confound between-person and within-person relations either partially or entirely, leading to inaccurate results. Furthermore, in the increasingly complex model variants that continue to be developed, what is not easily appreciated is how substantial differences in interpretation can be created by what appear to be trivial differences in model specification. In the present work, we aimed to (a) help analysts become better acquainted with the some of the more common model variants that fall under this larger umbrella, and (b) explicate what characteristics of one's data and research questions should be considered in selecting a model. Supplementary Materials include annotated model syntax and output using Mplus, lavaan in R, and sem in Stata to help translate these concepts into practice.