The mixed or heterogeneous multinomial logit (MIXL) model has become popular in a number of fields, especially marketing, health economics, and industrial organization. In most applications of the model, the vector of consumer utility weights on product attributes is assumed to have a multivariate normal (MVN) distribution in the population. Thus, some consumers care more about some attributes than others, and the IIA property of multinomial logit (MNL) is avoided (i.e., segments of consumers will tend to switch among the subset of brands that possess their most valued attributes). The MIXL model is also appealing because it is relatively easy to estimate. Recently, however, some researchers have argued that the MVN is a poor choice for modelling taste heterogeneity. They argue that much of the heterogeneity in attribute weights is accounted for by a pure scale effect (i.e., across consumers, all attribute weights are scaled up or down in tandem). This implies that choice behaviour is simply more random for some consumers than others (i.e., holding attribute coefficients fixed, the scale of their error term is greater). This leads to a “scale heterogeneity” MNL model (S-MNL). Here, we develop a generalized multinomial logit model (G-MNL) that nests S-MNL and MIXL. By estimating the S-MNL, MIXL, and G-MNL models on 10 data sets, we provide evidence on their relative performance. We find that models that account for scale heterogeneity (i.e., G-MNL or S-MNL) are preferred to MIXL by the Bayes and consistent Akaike information criteria in all 10 data sets. Accounting for scale heterogeneity enables one to account for “extreme” consumers who exhibit nearly lexicographic preferences, as well as consumers who exhibit very “random” behaviour (in a sense we formalize below).choice models, mixture models, consumer heterogeneity, choice experiments
We provide a user guide on the analysis of data (including best-worst and best-best data) generated from discrete choice experiments (DCEs), comprising a theoretical review of the main choice models followed by practical advice on estimation and post estimation. We also provide a review of standard software. In providing this guide we endeavor not only to provide guidance on choice modeling, but to do so in a way that provides researchers to the practicalities of data analysis. We argue that choice of modeling approach depends on: the research questions; study design and constraints in terms of quality/quantity of data and that decisions made in relation to analysis of choice data are often interdependent rather than sequential. Given the core theory and estimation of choice models is common across settings, we expect the theoretical and practical content of this paper to be useful not only to researchers within but also beyond health economics.
Compliance with Ethical StandardsNo funding was received for the preparation of this paper. Emily Lancsar is funded by an ARC Fellowship (DE1411260). Emily Lancsar, Denzil Fiebig and Arne Risa Hole have no conflicts of interest.
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Key Points for Decision Makers We provide a user guide on the analysis of data, including best-worst and best-best data, generated from DCEs, addressing the questions of DCE We provide a theoretical overview of the main choice models and review three standard statistical software packages: Stata; Nlogit; and Biogeme. Choice of modeling approach depends on the research questions; study design and constraints in terms of quality/quantity of data and decisions made in relation to analysis of choice data are often interdependent rather than sequential. A health based DCE example for which we provide the data and estimation code is used throughout to demonstrate the data set up, variable coding, various model estimation and post estimation approaches.3
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