ABSTRACT
Standard versions of the normal linear model and general linear models assume additive and linear predictor effects in the regression mean, and a constant variance. While linear regression effects are often suitable, nonlinear predictor effects and heteroscedasticity are common in areas as diverse as economics, hydrology (Qian et al., 2005), and epidemiology (Natario and Knorr-Held, 2003). Simple nonlinear forms such as polynomials or logarithmic transformations of predictors or responses may often be suitable, but arguably are seeking to provide a global parameterization when local flexibility is needed to reproduce observed reponse patterns (Beck and Jackman, 1998). In some applications there may be a theoretical basis for a particular form of nonlinearity, though some elements of specification will be uncertain-see Borsuk and Stow (2000) for an example on biochemical oxygen demand and Meyer and Millar (1998) for models of fishery stock.
