ABSTRACT
The sciences construct theories of natural processes. Eventually these theories are expressed formally, as mathematical models. Such models are specialized, make precise predictions, and can fail in equally precise ways. Being wrong in precise ways is useful, because the failures borrow meaning from the cause and effect relationships built into the models. Applied statistics has to apply to all the sciences, and so it is often much vaguer about models. Instead it focuses on average performance, regardless of the model. The generalized linear models in the preceding chapters are not credible scientific models of most natural processes. One of the major advantages of having a scientifically inspired model is that the parameters have meanings. The chapter highlights one of the reasons that generalized linear models are so powerful. Lots of natural relationships are GLM relationships, on a specific scale of measurement.
