An extended quasi-likelihood function. (English) Zbl 0621.62078

Nelder, J. A.; Pregibon, D.

Biometrika 74, 221-232 (1987).

The introduction by R. W. M. Wedderburn [Biometrika 61, 439-447 (1974; Zbl 0292.62050)] of quasi-likelihood for general linear models greatly widened their scope by allowing the full distributional assumption about the random component in the models to be replaced by a much weaker assumption in which only the first and second moments were defined.
The present authors introduce an extended quasi-likelihood function which allows for the comparison of various forms of all the components of a generalized linear model, i.e. the linear predictor, the link function, and the variance function. The theory is illustrated by three examples.

Reviewer: A.N.Philippou

MSC:

62J99	Linear inference, regression
62J05	Linear regression; mixed models
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

data transformation; exponential family; saddlepoint approximation; second-moment assumptions; general linear models; extended quasi- likelihood function; generalized linear model; linear predictor; link function; variance function; examples

Citations:

Zbl 0292.62050