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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COMBI's quasi-likelihood estimation approach is robust to missing data values.
“The quasi-likelihood estimation approach is also robust to missing data values.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · cites this paper as Wedderburn, 1974
Provided that data are missing completely at random (MCAR) or missing at random (MAR), COMBI's quasi-likelihood estimation procedure yields unbiased parameter estimates based on all complete or partial observations.
“Provided that the data are missing completely at random (MCAR) or missing at random (MAR), the quasi-likelihood estimation procedure yields unbiased parameter estimates based on all (complete or partial) observations.”
From Missing data in multi-omics integration: Recent advances through artificial intelligence (2023) · 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
- JSTOR
- Published
- 1974-12
- Volume
- 61
- Issue
- 3
- Pages
- 439
- ISSN
- 0006-3444 (ISSN-L)
- 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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