Misapplications Reviews: The Linear Model and Some of its Friends

Most university courses in mathematical programming and multivariate statistics start with a treatment of the linear model. This makes pedagogical sense, for the underlying theory is both conceptually easier and more fully developed in the linear than the nonlinear case. Moreover, linear relationships abound in nature (for example, the gravitational attraction of an object is proportional to its mass).

We MS/OR types know that the world can be cruel, and that an error in functional form can both reverse the sign and distort the magnitude of the effect one is trying to estimate. Thus I have sometimes asked researchers, both verbally and in writing, why they thought it appropriate to proceed with a linear model. Rarely has the answer been a theoretical defense of an assumption of proportionality; the more typical response is a withering stare, a dose of content-free jargon, or an all-purpose argument that, while thought-provoking, is ultimately dissatisfying. Often I get a (er … linear) combination of these things.