Falsifying causal hypotheses in time series models with conditional-independence tests

James T Thorson, Cole C. Monnahan, Lauren A. Rogers

Ecologists often use time-series models to approximate dynamics arising from density dependence, species interactions, community synchrony, and other processes.  Dynamic structural equation models (DSEM) can represent simultaneous and lagged interactions among variables with missing data, and therefore encompasses a wide family of analyses (linear regression, vector autoregressive models, and dynamic factor analysis).  However, before interpreting a DSEM as a causal model, analysts should first test whether its assumptions about conditional independence are inconsistent with available data (i.e., attempt to falsify the model).  

In site-replicated and phylogenetic contexts, ecologists seek to falsify causal assumptions by testing implied conditional-independence relationships using a directional-separation (“d-sep”) test, but this has not been demonstrated using time-series analysis of ecological systems involving simultaneous and lagged interactions.  Here, we propose a time-series d-sep test and use a simulation experiment and case studies to explore its performance.  

The simulation confirms that this test results in a uniform p-value when using a correct causal model, and a low p-value (i.e., a decision to reject a model) when the causal model is incorrect.  As expected, time-series that are short or have a large proportion of missing data have less power to reject an incorrect model.  In a previously published analysis involving wolf-moose interactions in Isle Royale, the test supports top-down control but cannot distinguish whether bottom-up control is supported.  In a novel application involving pollock in the Gulf of Alaska, the test supports a conceptual model where temperature drives spawning phenology, which subsequently affects availability to a spawning survey.   

We conclude that d-sep is a useful test to falsify the conditional-independence assumptions of a time-series model.  It is therefore complementary to other methods used to validate causal inference (i.e., controlled experiments, ecological theory, and system knowledge).