VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics.
Complex systems, such as in brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often difficult. We propose using a Vector Autoregressive model with eXogenous input (VARX) to c...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0313875 |
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| _version_ | 1841533197767147520 |
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| author | Lucas C Parra Aimar Silvan Maximilian Nentwich Jens Madsen Vera E Parra Behtash Babadi |
| author_facet | Lucas C Parra Aimar Silvan Maximilian Nentwich Jens Madsen Vera E Parra Behtash Babadi |
| author_sort | Lucas C Parra |
| collection | DOAJ |
| description | Complex systems, such as in brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often difficult. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. Whereas this model aligns with Granger's statistical formalism for testing "causal relations", the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of these systems. For instance, in neural recordings we find that prolonged response of the brain can be explained as a short exogenous effect, followed by prolonged internal recurrent activity. In recordings of human physiology, we find that the model recovers established effects such as eye movements affecting pupil size and a bidirectional interaction of respiration and heart rate. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption: https://github.com/lcparra/varx. |
| format | Article |
| id | doaj-art-d61d443f05ff45a3a480b68f2b901be7 |
| institution | Kabale University |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-d61d443f05ff45a3a480b68f2b901be72025-01-17T05:31:31ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01201e031387510.1371/journal.pone.0313875VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics.Lucas C ParraAimar SilvanMaximilian NentwichJens MadsenVera E ParraBehtash BabadiComplex systems, such as in brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often difficult. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. Whereas this model aligns with Granger's statistical formalism for testing "causal relations", the connection between the two is not widely understood. Here, we bridge this gap by providing fundamental equations, user-friendly code, and demonstrations using simulated and real-world data from neuroscience, physiology, sociology, and economics. Our examples illustrate how the model avoids spurious correlation by factoring out external influences from internal dynamics, leading to more parsimonious explanations of these systems. For instance, in neural recordings we find that prolonged response of the brain can be explained as a short exogenous effect, followed by prolonged internal recurrent activity. In recordings of human physiology, we find that the model recovers established effects such as eye movements affecting pupil size and a bidirectional interaction of respiration and heart rate. We also provide methods for enhancing model efficiency, such as L2 regularization for limited data and basis functions to cope with extended delays. Additionally, we analyze model performance under various scenarios where model assumptions are violated. MATLAB, Python, and R code are provided for easy adoption: https://github.com/lcparra/varx.https://doi.org/10.1371/journal.pone.0313875 |
| spellingShingle | Lucas C Parra Aimar Silvan Maximilian Nentwich Jens Madsen Vera E Parra Behtash Babadi VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. PLoS ONE |
| title | VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. |
| title_full | VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. |
| title_fullStr | VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. |
| title_full_unstemmed | VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. |
| title_short | VARX Granger analysis: Models for neuroscience, physiology, sociology and econometrics. |
| title_sort | varx granger analysis models for neuroscience physiology sociology and econometrics |
| url | https://doi.org/10.1371/journal.pone.0313875 |
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