Implications of linear versus dummy coding for pooling of information in hierarchical models

Abstract

Hierarchical models have become a workhorse tool in applied marketing research, particularly in the context of conjoint choice experiments. The industry has been pushing for ever more complex studies and 50+ random effects in a study are very common today. At the same time, respondent time and motivation is scarce as ever. Consequently, inference about high dimensional random effects critically depends on efficient pooling of information across respondents. In this paper we show how restrictions on the functional form of effects translate into more efficient pooling of information across respondents, compared to flexible functional forms achieved through categorical coding. We develop our argument contrasting the most restrictive functional form, i.e. linearity to categorical coding and then generalize to simple ordinal constraints. We close with suggestions on how to improve the pooling of information when definite functional form assumptions cannot be justified a priori, for example in studies that measure preferences over large sets of brands.