Generalized linear models in soil science

Classical linear models are easy to understand and fit. However, when assumptions are not met, violence should not be used on the data to force them into the linear mould. Transformation of variables may allow successful linear modelling, but it affects several aspects of the model simultaneously. In particular, it can interfere with the scientific interpretation of the model. Generalized linear models are a wider class, and they retain the concept of additive explanatory effects. They provide generalizations of the distributional assumptions of the response variable, while at the same time allowing a transformed scale on which the explanatory effects combine. These models can be fitted reliably with standard software, and the analysis is readily interpreted in an analogous way to that of linear models. Many further generalizations to the generalized linear model have been proposed, extending them to deal with smooth effects, non-linear parameters, and extra components of variation. Though the extra complexity of generalized linear models gives rise to some additional difficulties in analysis, these difficulties are outweighed by the flexibility of the models and ease of interpretation. The generalizations allow the intuitively more appealing approach to analysis of adjusting the model rather than adjusting the data.