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Regression Analysis of Poisson-Distributed Data
Abstract
The principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution. The maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the Poisson assumption. Computationally, both of these estimation procedures are equivalent to a properly weighted least squares analysis. Approximate tests of the assumed Poisson variation and “goodness of fit” of the data to the model are proposed. Applications of the estimation procedure to linear and nonlinear regression models are discussed, and numerical examples are presented.
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Citations
Cites
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
Cited by
Li, Q., Maggitti, P. G., Smith, K. G., Tesluk, P. E., & Katila, R. (2013) · Academy of Management Journal · doi:10.5465/amj.2010.0844 · Cited by 438
Generalized poisson regression model
Consul, P. C., & Famoye, F. (1992) · Communications in Statistics - Theory and Methods · doi:10.1080/03610929208830766 · Cited by 388
Hazard rate ratio and prospective epidemiological studies
Symons, M. J., & Moore, D. T. (2002) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(02)00443-2 · Cited by 347
Tests for Detecting Overdispersion in Poisson Regression Models
Dean, C., & Lawless, J. F. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478792 · Cited by 342
Tests of Hypotheses in Overdispersed Poisson Regression and other Quasi-Likelihood Models
Breslow, N. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476236 · Cited by 288
Metadata
- Authors
- Frome, E. L., Kutner, M. H., & Beauchamp, J. J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1973-12
- Volume
- 68
- Issue
- 344
- Pages
- 935-940
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2081969704
- Cited by
- 184
- References
- 1
- FWCI
- 1.23
- Type
- journal article
- Language
- en
- Open access
- closed
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- Frome, E. L., Kutner, M. H., & Beauchamp, J. J. (1973). Regression Analysis of Poisson-Distributed Data. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1973.10481449
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
