Generalised linear models for prediction: some principles, some programs and some practice

Despite a history now over 30 years long, the adoption of generalised linear models (GLMs) remains patchy: they are well known in several fields, but used little if at all in many others. One major advantage of GLMs is that they return predictions on the scale of the response. The use of link functions avoids the need for prior transformation of the response, for back-transformation of predictions, and above all for bias corrections to back-transformations, whether systematic or ad hoc. Case studies from environmental applications (suspended sediment concentrations of rivers, heights of forest trees) are introduced in which predictions on the response scale are of paramount scientific and practical interest. Heavy use is made of a suite of Stata programs written by the author producing graphic and numeric diagnostics after regression-type models, which extend and complement commands in official Stata. Most of these programs have uses beyond GLMs and they will also be discussed directly.