Dummy coding vs effects coding for categorical variables: clarifications and extensions

This note revisits the issue of the specification of categorical variables in choice models, in the context of ongoing discussions that one particular normalisation, namely effects coding, is superior to another, namely dummy coding. For an overview of the issue, the reader is referred to Hensher et al. (2015, see pp. 60-69) or Bech and Gyrd-Hansen (2005). We highlight the theoretical equivalence between the dummy and effects coding and show how parameter values from a model based on one normalisation can be transformed (after estimation) to those from a model with a different normalisation. We also highlight issues with the interpretation of effects coding, and put forward a more well-defined version of effects coding.