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A geometric approach to assess bias due to omitted covariates in generalized linear models
Abstract
Misspecifying generalized linear models by omitting covariates associated with the response can result in seriously biased estimates of the effects of the included covariates. For certain models, such bias can occur even when the omitted covariate is independent of the included covariates, as in studies with randomized treatment assignment. This paper presents a geometric approach to assess the direction of the bias resulting from omitted covariates and develop intuition about the effects of omitted covariates. We show that the direction of the bias depends simply on geometric properties of the link function. We present an expression for the magnitude of the bias and the results of simulations which corroborate these findings. We also consider an extension of the methods to assess the effects of omitted covariates which are correlated with those included.
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Citations
Cited by
Daniel, R., Zhang, J., & Farewell, D. (2021) · Biometrical Journal · doi:10.1002/bimj.201900297 · Cited by 167
Including known covariates can reduce power to detect genetic effects in case-control studies
Pirinen, M., Donnelly, P., & Spencer, C. C. A. (2012) · Nature Genetics · doi:10.1038/ng.2346 · Cited by 117
Noncollapsibility and its role in quantifying confounding bias in logistic regression
Schuster, N. A., Twisk, J. W. R., ter Riet, G., Heymans, M. W., & Rijnhart, J. J. M. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01316-8 · Cited by 61
Linear and Non-Linear Regression Methods in Epidemiology and Biostatistics
Vittinghoff, E., McCulloch, C. E., Glidden, D. V., & Shiboski, S. C. (2011) · Essential Statistical Methods for Medical Statistics · doi:10.1016/b978-0-444-53737-9.50006-2 · Cited by 6
Metadata
- Authors
- NEUHAUS, J. M., & JEWELL, N. P.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1993
- Volume
- 80
- Issue
- 4
- Pages
- 807-815
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W1979102876
- Cited by
- 159
- References
- 0
- FWCI
- 2.32
- Type
- journal article
- Language
- en
- Open access
- closed
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- NEUHAUS, J. M., & JEWELL, N. P. (1993). A geometric approach to assess bias due to omitted covariates in generalized linear models. Biometrika. https://doi.org/10.1093/biomet/80.4.807
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