Heterogeneity In Choice Models Research Articles

Heterogeneity in choice models of addiction: the role of context.

Theories of addiction guide scientific progress, funding priorities, and policy development and ultimately shape how people experiencing or recovering from addiction are perceived and treated. Choice theories of addiction are heterogenous, and different models have divergent implications. This breeds confusion among laypeople, scientists, practitioners, and policymakers and reduces the utility of robust findings that have the potential to reduce the global burden of addiction-associated harms. Here we differentiate classes of choice models and articulate a novel framing for a class of addiction models, called contextual models, which share as a first principle the influence of the environment and other contextual factors on behavior within discrete choice contexts. These models do not assume that all choice behaviors are voluntary, but instead that both proximal and distal characteristics of the choice environment-and particularly the benefits and costs of both drug use and non-drug alternatives-can influence behavior in ways that are outside of the awareness of the individual. From this perspective, addiction is neither the individual's moral failing nor an internal uncontrollable urge but rather is the result of environmental contingencies that reinforce the behavior. Contextual models have implications for guiding research, practice, and policy, including identification of novel target mechanisms while also improving existing interventions.

A Bayesian Semiparametric Approach for Endogeneity and Heterogeneity in Choice Models

Marketing variables that are included in consumer discrete choice models are often endogenous. Extant treatments using likelihood-based estimators impose parametric distributional assumptions, such as normality, on the source of endogeneity. These assumptions are restrictive because misspecified distributions have an impact on parameter estimates and associated elasticities. The normality assumption for endogeneity can be inconsistent with some marginal cost specifications given a price-setting process, although they are consistent with other specifications. In this paper, we propose a heterogeneous Bayesian semiparametric approach for modeling choice endogeneity that offers a flexible and robust alternative to parametric methods. Specifically, we construct centered Dirichlet process mixtures (CDPM) to allow uncertainty over the distribution of endogeneity errors. In a similar vein, we also model consumer preference heterogeneity nonparametrically via a CDPM. Results on simulated data show that incorrect distributional assumptions can lead to poor recovery of model parameters and price elasticities, whereas the proposed semiparametric model is able to robustly recover the true parameters in an efficient fashion. In addition, the CDPM offers the benefits of automatically inferring the number of mixture components that are appropriate for a given data set and is able to reconstruct the shape of the underlying distributions for endogeneity and heterogeneity errors. We apply our approach to two scanner panel data sets. Model comparison statistics indicate the superiority of the semiparametric specification and the results show that parameter and elasticity estimates are sensitive to the choice of distributional forms. Moreover, the CDPM specification yields evidence of multimodality, skewness, and outlying observations in these real data sets. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1811 . This paper was accepted by J. Miguel Villas-Boas, marketing.

A Bayesian Semiparametric Approach for Endogeneity and Heterogeneity in Choice Models

Marketing variables that are included in consumer discrete choice models are often endogenous. Extant treatments using likelihood-based estimators impose parametric distributional assumptions, such as normality, on the source of endogeneity. These assumptions are restrictive as misspecified distributions have an impact on parameter estimates and associated elasticities. The normality assumption for endogeneity can be inconsistent with some marginal cost specifications given a price setting process, although being consistent with other specifications. In this paper we propose a heterogeneous Bayesian semiparametric approach for modeling choice endogeneity which offers a flexible and robust alternative to parametric methods. Specifically, we construct centered Dirichlet process mixtures (CDPM) to allow uncertainty over the distribution of endogeneity errors. In a similar vein, we also model consumer preference heterogeneity non-parametrically via a CDPM. Results on simulated data show that incorrect distributional assumptions can lead to poor recovery of model parameters and price elasticities, whereas, the proposed semiparametric model is able to robustly recover the true parameters in an efficient fashion. In addition, the CDPM offers the benefits of automatically inferring the number of mixture components that are appropriate for a given data set and is able to reconstruct the shape of the underlying distributions for endogeneity and heterogeneity errors. We apply our approach to two scanner panel data sets. Model comparison statistics indicate the superiority of the semiparametric specification and the results show that parameter and elasticity estimates are sensitive to the choice of distributional forms. Moreover, the CDPM specification yields evidence of multimodality, skewness, and outlying observations in these real data sets.

Accounting for scale heterogeneity within and between pooled data sources

There is growing interest in incorporating both preference heterogeneity and scale heterogeneity in choice models, as a way of capturing an increasing number of sources of utility amongst a set of alternatives. The extension of mixed logit to incorporate scale heterogeneity in a generalised mixed logit (GMXL) model provides a way to accommodate these sources of influence, observed and unobserved. The small but growing number of applications of the GMXL model have parameterized scale heterogeneity as a single estimate; however it is often the case that analysts pool data from more than one source, be it revealed preference (RP) and stated preference (SP) sources, or multiple SP sources, inducing the potential for differences in the scale factor between the data sources. Existing practice has developed ways of accommodating scale differences between data sources by adopting a scale homogeneity assumption within each data source (e.g., the nested logit trick) that varies between data sources. This paper extends the state of the art by incorporating data-source specific scale differences in scale heterogeneity setting across pooled RP and SP data set. An example of choice amongst RP and SP transport modes (including two ‘new’ SP modes) is used to obtain values of travel time savings that vary significantly between a model that accounts for scale heterogeneity differences within pooled RP and SP data, and the other where differences in scale heterogeneity is also accommodated between RP and SP data.

Assessing Heterogeneity in Discrete Choice Models Using a Dirichlet Process Prior

The finite normal mixture model has emerged as a dominant methodology for assessing heterogeneity in choice models. Although it extends the classic mixture models by allowing within component variablility, it requires that a relatively large number of models be separately estimated and fairly difficult test procedures to determine the “correct” number of mixing components. We present a very general formulation, based on Dirichlet Process Piror, which yields the number and composition of mixing components a posteriori, obviating the need for post hoc test procedures and is capable of approximating any target heterogeneity distribution. Adapting Stephens’ (2000) algorithm allows the determination of ‘substantively’ different clusters, as well as a way to sidestep problems arising from label-switching and overlapping mixtures. These methods are illustrated both on simulated data and A.C. Nielsen scanner panel data for liquid detergents. We find that the large number of mixing components required to adequately represent the heterogeneity distribution can be reduced in practice to a far smaller number of segments of managerial relevance.