What do we mean by a statistical model?

Abstract

Statisticians are too often satisfied by fitting data rather than investigating the process out of which the data arose. The assumptions on which they base their models may be quite unrealistic, and while it is true that a model should not be more complicated than necessary, neither should it be too simple. Ways of approaching several sets of data from different areas of clinical medicine are considered, and different attitudes to the purpose of modelling highlighted. The transition from smoothing data, through fitting curves, to modelling underlying processes is discussed.

An Overview of Models of Cell Proliferation

“…The data are summarised in Figure 1, which also shows the result of fitting a Gompertz equation and a logistic equation to the data. These data have been discussed previously (Appleton, 1995) but the units on the vertical axis there should read 'g', not 'mg'. It is not possible to distinguish with much certainty between the adequacy of these models by reference to the data, though the Gompertz does have a smaller residual standard deviation: 0.205 compared to 0.265, both of the fits being to the natural logarithms of the tumour weights.…”