Abstract
Data arising from social systems is often highly complex,
involving non-linear relationships between the macro-level variables that
characterize these systems. We present a method for analyzing this type of
longitudinal or panel data using differential equations. We identify the best
non-linear functions that capture interactions between variables, employing
Bayes factor to decide how many interaction terms should be included in the
model. This method punishes overly complicated models and identifies models
with the most explanatory power. We illustrate our approach on the classic
example of relating democracy and economic growth, identifying non-linear
relationships between these two variables. We show how multiple variables and
variable lags can be accounted for and provide a toolbox in R to implement our
approach.