Source code for R tutorials and dataset for empirical case study on Malurus elegans (red-winged fairy wren)

Biological processes exhibit complex temporal dependencies due to the sequential nature of allocation decisions in organisms’ life-cycles, feedback loops, and two-way causality. Consequently, longitudinal data often contain cross-lags: the predictor variable depends on the response variable of the previous time-step. Although statisticians have warned that regression models that ignore such covariate endogeneity in time series are likely to be inappropriate, this has received relatively little attention in biology. Furthermore, the resulting degree of estimation bias remains largely unexplored.

We use a graphical model and numerical simulations to understand why and how regression models that ignore cross-lags can be biased, and how this bias depends on the length and number of time series. Ecological and evolutionary examples are provided to illustrate that cross-lags may be more common than is typically appreciated and that they occur in functionally different ways.

We show that...