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Quasi-Likelihood Functions, Generalized Linear Models, and the Gauss-Newton Method

Wedderburn, R. W. M.·1974·Biometrika

DOI 10.2307/2334725

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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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Authors: Wedderburn, R. W. M.
Affiliations: Rothamsted Research (GB)
Corresponding author: Wedderburn, R. W. M.
Venue: Biometrika
Publisher: JSTOR
Published: 1974-12
Volume: 61
Issue: 3
Pages: 439
ISSN: 0006-3444 (ISSN-L)
DOI: 10.2307/2334725
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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Quasi-Likelihood Functions, Generalized Linear Models, and the Gauss-Newton Method

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