Statistical model specification

In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income ${\displaystyle y}$ together with years of schooling ${\displaystyle s}$ and on-the-job experience ${\displaystyle x}$, we might specify a functional relationship ${\displaystyle y=f(s,x)}$ as follows:^[1]

${\displaystyle \ln y=\ln y_{0}+\rho s+\beta _{1}x+\beta _{2}x^{2}+\varepsilon }$

where ${\displaystyle \varepsilon }$ is the unexplained error term that is supposed to comprise independent and identically distributed Gaussian variables.

The statistician Sir David Cox has said, "How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis".^[2]