Extending the Generalized Multinomial Logit Model: Error Scale and Decision-Maker Characteristics

Abstract

This essay contributes to the development of models that allow for heterogeneity across respondents in the error scale of the multinomial logit model. The potential to explain respondent heterogeneity by differences in error scale has been recognized for some time (Louviere 2001), but models that allow for continuous error scale heterogeneity have only recently been developed (Sonnier, Ainslie and Otter 2007, Keane et al. 2009). The most general of these models is the “Generalized Multinomial Logit Model” (G-MNL), which allows for heterogeneity both in error scale and all attribute preferences, including the price attribute (Keane et al. 2009). We further develop the G-MNL by proposing a Bayesian estimation strategy, allowing for straightforward incorporation of decision-maker characteristics as covariates to individual-level error scale, in a way that is computationally tractable. In a data set on personal computer (PC) choices in a survey setting (Lenk et al. 1996), we find that respondents who are older have higher average error scale indicating that they make less reliable decisions than those who are younger. Respondents who perceive themselves to be expert when it comes to making PC choices have lower average error scale, indicating that they make more reliable choices. These findings are consistent with recent theorizing on the relationship between cognitive resources and error scale (Swait and Adamowicz 2001). We also facilitate the use of G-MNL in practice by empirically exploring the data requirements for obtaining accurate estimates of the G-MNL and find that estimating this model requires a somewhat larger number of respondents and a larger number of observed choices per respondent than is typical in commercial market research.

Keywords: Error Scale, Generalized Multinomial Logit, Discrete Choice, Bayesian MCMC

JEL Classification: C11, C25