R.W.M. Wedderburn's research while affiliated with Station X and other places

Publications (5)

Article
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 qua...
Article
A modification of the method of Nelder and Wedderburn (1972) is given for fitting models with the same error distributions as discussed there but with the systematic part of the models specified in terms of constraints. It is possible to fit these by the method described by Nelder and Wedderburn using iterative weighted regression, but it turns out...
Article
For forty-one soils (pH > 5.0) from southern England and eastern Australia, the Langmuir equation was an excellent model for describing P adsorption from solutions < 10-3M P, if it was assumed that adsorption occurs on two types of surface of contrasting bonding energies. For most of these soils, which were relatively undersaturated with P, this eq...
Article
The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- l...

Citations

... Achieving the interpretability from flexible statistical models as e.g. Generalized Linear Models (GLMs) (Nelder & Wedderburn, 1972) or Generalized Additive Models (GAMs) (Hastie, 2017), in deep neural networks, however, is inherently difficult. Recently, Agarwal et al. (2021) introduced Neural Additive Models (NAMs), a framework that models all features individually and thus creates visual interpretability of the single features. ...
... , σ k . In particular, if we let X (k) and Y (k) denote zero-mean jointly Gaussian variables with the same marginals as X and Y , respectively, but covariance 55 ...
... According to DSL isotherm, the low-energy surfaces usually have a low Langmuir constant (K 2 ) and a high adsorption capacity (b 2 ), while the high-energy surfaces have a high Langmuir constant (K 1 ) and a low adsorption capacity (b 2 ). Arsenic is loosely held on the low-energy surfaces and tightly held on the high-energy surfaces (Holford et al., 1974;Jiang et al., 2005b). For soils 1, 2, 3, and 4, the adsorption capacities of the high-energy surfaces (without competition) were 86.2, 83.3, 71.4, and 69.5 mg/kg and the adsorption capacities of the low-energy surfaces were 663, 496, 375.5, and 223 mg/kg, respectively. ...
... FLR models assume that the outcome variable is a proportion of the interval from 0 to 1, so we made a linear transformation of the outcome (dividing by 365 days). FLR was first described by Wedderburn (1974), generalized by McCullagh (1983) and rediscovered by Papke and Wooldridge (1996). FLR belongs to the family of generalized linear models, is based on quasi-maximum likelihood estimators, and is very similar to binary logistic regression. ...