Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method
Abstract
To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-parameter exponential family is the weakest sort of distributional assumption that can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal with maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder & Wedderburn (1972).
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Using a quasi-likelihood method ("Quasipoisson") provided unbiased type I error rates, like in the Gaussian models.
“Using a quasi-likelihood method (“Quasipoisson”, Wedderburn, 1974) provided unbiased type I error rates, like in the Gaussian models (Fig. 3)”
From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Wedderburn, 1974
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- Authors
- WEDDERBURN, R. W. M.
- Affiliations
- Rothamsted Research (GB)
- Corresponding author
- WEDDERBURN, R. W. M.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1974
- Volume
- 61
- Issue
- 3
- Pages
- 439-447
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W1979159029
- Cited by
- 2,122
- References
- 0
- Citations by year
- 2026: 18 · 2025: 40 · 2024: 58 · 2023: 54 · 2022: 50 · 2021: 87 · 2020: 72 · 2019: 78 · 2018: 111 · 2017: 70 · 2016: 84 · 2015: 64 · 2014: 86 · 2013: 80 · 2012: 133
- FWCI
- 2.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Rothamsted Repository (Rothamsted Repository) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- generalized linear models, Gauss-Newton method, exponential family, mean-variance relationship, nonlinear least squares, distributional assumptions
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