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Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data
Open accessAbstract
Correlation does not imply causation; but often, observational data are the only option, even though the research question at hand involves causality. This article discusses causal inference based on observational data, introducing readers to graphical causal models that can provide a powerful tool for thinking more clearly about the interrelations between variables. Topics covered include the rationale behind the statistical control of third variables, common procedures for statistical control, and what can go wrong during their implementation. Certain types of third variables—colliders and mediators—should not be controlled for because that can actually move the estimate of an association away from the value of the causal effect of interest. More subtle variations of such harmful control include using unrepresentative samples, which can undermine the validity of causal conclusions, and statistically controlling for mediators. Drawing valid causal inferences on the basis of observational data is not a mechanistic procedure but rather always depends on assumptions that require domain knowledge and that can be more or less plausible. However, this caveat holds not only for research based on observational data, but for all empirical research endeavors.
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“explaining away mechanisms of interest and is thus discouraged in correlational modeling (33).”
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“Specifically, conditioning on a collider can open a previously closed path in the network, potentially leading to biased estimates and false causal interpretations (Rohrer, 2018).”
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InfluentialCausal discovery and the problem of psychological interventions
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“From a statistical point of view, restricted sampling can lead to selection bias which in turn can lead to confounding (Bareinboim and Pearl 2012; Elwert and Winship 2014; Fiedler 2000; Rohrer 2018).”
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“To the extent that researchers view them as nuisance variables, confounds may be treated as covariates in a model to filter out extraneous variability in scores (Rohrer, 2018).”
BackgroundPrecise Answers to Vague Questions: Issues With Interactions
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“1999), psychology (Rohrer 2018), and medical research (Richens et al.”
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Why most psychological research findings are not even wrong
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“X j denotes that an intervention to change the value of X i will lead to a change in the probability distribution of X j (for an accessible, more elaborate introduction to the use of DAGs in causal inference see, amongst others Hernan & Robins, 2010; Pearl et al., 2016; Rohrer, 2018).”
BackgroundTemperament and brain networks of attention
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“Even though the study findings were based on directed acyclic graphs to infer causality [37], this study remains cross-sectional in nature and true causality cannot be determined.”
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“This includes fields like economics (e.g., Angrist & Pischke, 2010), political science (e.g., Samii, 2016), sociology (e.g., Gangl, 2010), and psychology (e.g., Rohrer, 2018).”
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“A usual approach to remove such spurious relationships in regression analyses is to include confounders as covariates in regression models (Rohrer, 2018).”
BackgroundPhase angle as a marker of muscle quality: A systematic review and meta-analysis
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Hiwar, W., King, M., Shuweihdi, F., Fletcher, L. A., Dancer, S. J., & Noakes, C. J. (2021) · Indoor Air · doi:10.1111/ina.12846 · Cited by 77
Moral values predict county-level COVID-19 vaccination rates in the United States.
Reimer, N. K., Atari, M., Karimi-Malekabadi, F., Trager, J. P., Kennedy, B., Graham, J., & Dehghani, M. (2022) · American Psychologist · doi:10.1037/amp0001020 · Cited by 73
Foundations and Future Directions for Causal Inference in Ecological Research
Siegel, K., & Dee, L. E. (2025) · Ecology Letters · doi:10.1111/ele.70053 · Cited by 85
Future Directions in the Study and Treatment of Parent–Child Separation
Humphreys, K. L. (2018) · Journal of Clinical Child & Adolescent Psychology · doi:10.1080/15374416.2018.1534209 · Cited by 81
“…variables, such practices are likely to be problematic when the “ covariates ” are actually mechanisms (e.g., covarying for reported distress following separation in examining the association between parent – child separation and subsequent psychopathology; see Kraemer, 2015; Rohrer, 2018).”
BackgroundInfluentialMader, N., Arslan, R. C., Schmukle, S. C., & Rohrer, J. M. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2212154120 · Cited by 71
“Here, the observed mean level of negative emotion is an outcome of differences in emotional varia-bility—thus, statistical adjustment for it may even induce over-control bias (14) and move estimates away from the true association between neuroticism and emotional variability.”
Self-citationCHIELD: the causal hypotheses in evolutionary linguistics database
Roberts, S. G., Killin, A., Deb, A., Sheard, C., Greenhill, S. J., Sinnemäki, K. T.-K., Segovia‐Martín, J., Nölle, J., Berdičevskis, A., Humphreys-Balkwill, A., et al. (2020) · Journal of Language Evolution · doi:10.1093/jole/lzaa001 · Cited by 70
“Causal inference is an approach to thinking about causality (Pearl, 2000; Pearl & Mackenzie, 2018; Rohrer, 2018) that uses graphical tools - causal graphs - to depict models of causal processes.”
BackgroundMethodInfluentialMichaelson, L., & Munakata, Y. (2020) · Psychological Science · doi:10.1177/0956797619896270 · Cited by 67
Bartram, D. (2021) · Social Indicators Research · doi:10.1007/s11205-020-02586-3 · Cited by 74
“Inclusion of intervening variables, in contrast, will introduce/ exacerbate bias (sometimes called “overcontrol bias”, e.g. Rohrer 2018, or “included variable bias”, York 2018).”
BackgroundThe APC-barrier and its effect on stratification in open access publishing
Klebel, T., & Ross‐Hellauer, T. (2023) · Quantitative Science Studies · doi:10.1162/qss_a_00245 · Cited by 85
“DAGs allow us to represent the causal assumptions of the studied phenomenon visually (Rohrer, 2018).”
BackgroundBehaviour Genetic Frameworks of Causal Reasoning for Personality Psychology
Briley, D. A., Livengood, J., & Derringer, J. L. (2018) · European Journal of Personality · doi:10.1002/per.2153 · Cited by 69
“However, several causal models may generate data whereby conscientiousness and life outcomes are correlated (Rohrer, 2018).”
BackgroundBertin, P., Nera, K., Hamer, K., Uhl-Haedicke, I., & Delouvée, S. (2021) · Group Processes & Intergroup Relations · doi:10.1177/1368430221992114 · Cited by 66
“Lastly, causality in the theoretical models should also be carefully defined, as controlling for a variable causally affected by the independent variable can not only result in spurious correlations, but also in the suppression of the effect under investigation (Rohrer, 2018).”
BackgroundPutting Psychology to the Test: Rethinking Model Evaluation Through Benchmarking and Prediction
Rocca, R., & Yarkoni, T. (2021) · Advances in Methods and Practices in Psychological Science · doi:10.1177/25152459211026864 · Cited by 61
“…standard regression methods—for example, treating regression coefficients as causal estimates without disclosing and defending causal assumptions (Rohrer, 2018; Watts, 2014; Watts et al., 2018) or concluding that a construct of interest has incremental validity over and above other constructs…”
MethodFoster, C. F. (2023) · International Journal of Research & Method in Education · doi:10.1080/1743727x.2023.2210063 · Cited by 129
“Interpretation is often perceived to be the most challenging aspect of quantitative research (Abelson 2012), and interpretation of quantitative data involves much more than merely distinguishing correlation from causation (see Rohrer 2018).”
BackgroundBridging maladaptive social self-beliefs and social anxiety: a network perspective
Heeren, A., Bernstein, E. E., & McNally, R. J. (2020) · Journal of Anxiety Disorders · doi:10.1016/j.janxdis.2020.102267 · Cited by 61
“Fourth, one cannot exclude the possibility that some of the non-zero edges in both GGM and DAG network models were artifacts due to conditioning on a collider variable (e.g., variables B in A → B ⟵ C; Rohrer, 2018).”
BackgroundKonuk, F. A., & Otterbring, T. (2023) · Journal of Retailing and Consumer Services · doi:10.1016/j.jretconser.2023.103531 · Cited by 68
Theory In, Theory Out: The Uses of Social Theory in Machine Learning for Social Science
Radford, J., & Joseph, K. (2020) · Frontiers in Big Data · doi:10.3389/fdata.2020.00018 · Cited by 58
Control variables and causal inference: a question of balance
York, R. (2018) · International Journal of Social Research Methodology · doi:10.1080/13645579.2018.1468730 · Cited by 62
“…and there are no other confounding factors.1 More complicated structures such as having more than three independent variables or complex causal pathways will only make the issues I raise here more problematic (Elwert & Winship, 2014; Morgan & Winship, 2015; Pearl et al., 2016; Rohrer, 2018).”
BackgroundMethodObsessive–compulsive symptoms in eating disorders: A network investigation
Meier, M., Kossakowski, J. J., Jones, P. J., Kay, B., Riemann, B. C., & McNally, R. J. (2019) · International Journal of Eating Disorders · doi:10.1002/eat.23196 · Cited by 61
Su, Y., Hu, M., Wang, Y., Zhang, H., He, C., Wang, Y., Wang, D., Wu, X., Zhuang, Y., Hong, S., et al. (2021) · Environmental Pollution · doi:10.1016/j.envpol.2021.118759 · Cited by 58
Power to Detect What? Considerations for Planning and Evaluating Sample SizePreprint
Giner‐Sorolla, R., Montoya, A. K., Aberson, C. L., Carpenter, T., Lewis, N. A., Bostyn, D. H., Conrique, B. G., Ng, B., Reifman, A. S., Schoemann, A. M., et al. (2023) · doi:10.31234/osf.io/rv3kw · Cited by 62
Garjani, A., Middleton, R., Hunter, R., Tuite-Dalton, K. A., Coles, A. J., Dobson, R., Duddy, M., Hughes, S., Pearson, O. R., Rog, D. J., et al. (2021) · Multiple Sclerosis and Related Disorders · doi:10.1016/j.msard.2021.102939 · Cited by 57
“B.1 and Appendix B) (Greenland et al., 1999; Rohrer, 2018).”
Korhonen, V. A., Mattsson, M. T., Inkinen, M., & Toom, A. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.01056 · Cited by 83
“Accordingly, we interpret the study findings as causal hypotheses, while bearing in mind that (1) conditioning on a common effect of two variables may introduce a spurious edge into the graph (Epskamp et al., 2018; Rohrer, 2018), (2) a clique in the network graph may indicate the presence of an unmodeled latent variab…”
BackgroundMethodInfluentialCausal inference on human behaviour
Bailey, D. H., Jung, A. J., Beltz, A. M., Eronen, M. I., Gische, C., Hamaker, E. L., Kording, K. P., Lebel, C., Lindquist, M. A., Moeller, J., et al. (2024) · Nature Human Behaviour · doi:10.1038/s41562-024-01939-z · Cited by 56
“Tools that help with such decision-making processes are increasingly available 7 .”
Self-citationScorpion species of medical importance in the Brazilian Amazon: a review to identify knowledge gaps
Martins, J. G., Santos, G. C., Procópio, R. E. D. L., Arantes, E. C., & Bordon, K. D. C. F. (2021) · The Journal of venomous animals and toxins including tropical diseases · doi:10.1590/1678-9199-jvatitd-2021-0012 · Cited by 55
“Because correlation does not imply causation [157], an experimental randomized trial would be required in order to support a conclusion of cause and effect.”
BackgroundAge-of-acquisition effects: A literature review.
Elsherif, M. M., Preece, E., & Catling, J. C. (2023) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/xlm0001215 · Cited by 54
Goldan, J., Nusser, L., & Gebel, M. (2022) · Child Indicators Research · doi:10.1007/s12187-022-09914-8 · Cited by 67
“To avoid overcontrol bias, we do not control for any mediating variables in the causal relationship between SEN status and schoolrelated SWB outcome variables because our interest is in the gross effect (Elwert & Winship, 2014; Rohrer, 2018).”
BackgroundMethodHoogeveen, S., Haaf, J. M., Bulbulia, J. A., Ross, R. M., McKay, R., Altay, S., Bendixen, T., Berniûnas, R., Cheshin, A., Gentili, C., et al. (2022) · Nature Human Behaviour · doi:10.1038/s41562-021-01273-8 · Cited by 62
A review of machine learning with small and limited data
Naser, M. Z. (2026) · Journal Of Big Data · doi:10.1186/s40537-025-01346-9 · Cited by 82
“Recognizing such limitations, recent work has aimed to advance causal inference to uncover the data distribution and map the underlying causal graph in synergy with small data [63, 64].”
Individual differences in mathematical cognition: a Bert's eye view
Smedt, B. D. (2022) · Current Opinion in Behavioral Sciences · doi:10.1016/j.cobeha.2022.101175 · Cited by 67
A correlation network analysis of dissociative experiences
Schimmenti, A., & Şar, V. (2019) · Journal of Trauma & Dissociation · doi:10.1080/15299732.2019.1572045 · Cited by 52
“Furthermore, common endogenous selection biases, such as nonresponse, attrition, and representativity bias (see Rohrer, 2018, for a review) would not apply to the current study only if it is correctly considered as a preliminary investigation on the cognitive and emotional dissociative processes…”
BackgroundInformation flow-based fuzzy cognitive maps with enhanced interpretability
Tyrovolas, M., Liang, X. S., & Stylios, C. D. (2023) · Granular Computing · doi:10.1007/s41066-023-00417-7 · Cited by 49
“Similarly, relying on the correlation coefficient is equally unreliable because it has been shown that correlation does not necessarily imply causality (Rohrer 2018).”
BackgroundReconsidering evidence of moral contagion in online social networks
Burton, J. W., Cruz, N., & Hahn, U. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01133-5 · Cited by 48
Trauma exposure and eating disorders: Results from a United States nationally representative sample
Convertino, A. D., Morland, L. A., & Blashill, A. J. (2022) · International Journal of Eating Disorders · doi:10.1002/eat.23757 · Cited by 49
“…(i.e., variables that may connote a common cause for both the independent variable and outcome) were controlled for, but collider variables (i.e., variables that are caused by both the independent variable and outcome) and mediator variables were not (see Rohrer, 2018 for further explanation).”
BackgroundLocal acceptance of solar farms: The impact of energy narratives
Scovell, M., McCrea, R., Walton, A., & Poruschi, L. (2023) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2023.114029 · Cited by 48
Metadata
- Authors
- Rohrer, J. M.
- Affiliations
- German Institute for Economic Research (DE)
- Corresponding author
- Rohrer, Julia M.
- ORCID
- Rohrer, Julia M.
- Venue
- Advances in Methods and Practices in Psychological Science
- Publisher
- SAGE Publications
- Published
- 2018-01-29
- Volume
- 1
- Issue
- 1
- Pages
- 27-42
- ISSN
- 2515-2459 (ISSN-L)
- 2515-2467
- OpenAlex
- W2776946813
- Cited by
- 1,002
- References
- 47
- Citations by year
- 2026: 124 · 2025: 145 · 2024: 150 · 2023: 147 · 2022: 122 · 2021: 132 · 2020: 137 · 2019: 31 · 2018: 14
- FWCI
- 65.35
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Methods and Practices in Psychological Science (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- OSF Preprints (OSF Preprints) (submittedVersion, cc-by)
- OSF Preprints (OSF Preprints) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- causal inference, observational data, causal graphical models, confounding, third variable, particle colliders, mediation, statistical control, causal assumptions, correlation versus causation
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