Quantifying Evidence for-and against-Granger Causality with Bayes Factors

Area of Science:

• Time Series Analysis
• Causal Inference
• Statistical Modeling

Background:

• Granger causality testing traditionally uses null hypothesis testing, limiting conclusions to rejecting or failing to reject the null hypothesis.
• Accepting the null hypothesis of no Granger causality is not possible within the classical framework, hindering applications like evidence integration and feature selection.
• Existing methods are insufficient for expressing evidence against an association or for handling complex, multilevel data structures.

Purpose of the Study:

• To derive and implement a Bayes factor for Granger causality within a multilevel modeling framework.
• To provide a continuously scaled evidence ratio for the presence or absence of Granger causality.
• To extend Granger causality testing to multilevel generalizations for improved inference with scarce or noisy data and population-level trends.

Main Methods:

• Derivation of the Bayes factor for Granger causality.
• Implementation within a multilevel modeling framework.
• Application to a daily life study exploring causal relationships in affect.

Main Results:

• The developed Bayes factor provides a continuous measure of evidence for Granger causality.
• The multilevel generalization facilitates robust inference in complex datasets.
• The approach allows for expressing evidence against Granger causality, overcoming limitations of traditional methods.

Conclusions:

• The Bayes factor for Granger causality offers a more flexible and informative approach to assessing temporal predictive relationships.
• Multilevel Granger causality testing enhances causal inference in complex, hierarchical data.
• This method is valuable for applications requiring nuanced evidence assessment, such as feature selection and evidence integration.