Model selection in regression analysis, regression diagnostics and prior knowledge: A book review article with comments from Anthony C. Atkinson, D.R. Cox And John McDonald

Abstract

Model selection of a regression model typically includes both selecting which variables to include in a model and the functional form of the relationship between the variables. In recent years regression diagnostics (a catch-all phrase that includes such topics as identifying influential observations) have been increasingly used as an aid in selecting a regression model. In evaluating the recent book Residuals and influence in regression, by Cook and Weisberg, Belsley argues that such analyses, while extremely useful, should not be used in a theoretical vacuum. Effective model building requires the analyst to make substantial use of any prior information relevant to the problem in hand. The commentators, while accepting the general thrust of Belsley's comments, are on the whole more sceptical — perhaps the prior knowledge is poor and in conflict with the data; perhaps the use of a wrong theory is more dangerous than ‘letting the data speak for themselves’.