Inference With Cross-Lagged Effects - Problems in Time and New Interpretations

The interpretation of cross-effects from vector autoregressive models to infer structure and causality amongst constructs is widespread and sometimes problematic. I first explain how hypothesis testing and regularization are invalidated when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps. I then describe an alternative interpretation of cross-effect parameters that incorporates correlated random changes for a potentially more realistic view of how process are temporally coupled. Using an example based on wellbeing data, I demonstrate how some classical concerns such as sign flipping and counter intuitive effect directions can disappear when using this combined deterministic / stochastic interpretation. Models that treat processes as continuously interacting offer both a resolution to the hypothesis testing problem, and the possibility of the combined stochastic / deterministic interpretation.