Nearly Linear Models Using General Link Functions

Summary

The major advantage of GLIM when fitting Generalised Linear Models is the ability to fit a succession of models by simply redefining the model statement. As such it is a major tool for data exploration. Several authors have used the facilities in GLIM to programme other problems which do not fall into the GLM class. However GLIM is not a good programming language. The successful attempts can be categorised by the fact that they allow the user this same flexibility to alter the model at the subsequent stages of the analysis.

There exists a large number of data analysis problems which satisfy the usual criteria for a GLM apart from a few extra nuisance parameters involved in the link function. The link function is nearly linear. Here we describe an approach to this class of problem which can be implemented simply on GLIM and which allows the linear component of the model to be altered using the standard GLIM model definition features.

Two examples are given. One fits a probit model with extra parameters for natural responsiveness. The other fits an inverse polynomial response function with two variables.