Research

Mediation analysis empirically investigates the process underlying the effect of an experimental manipulation on a dependent variable of interest. In the simplest mediation setting, the experimental treatment can affect the dependent variable through the mediator (indirect effect) and/or directly (direct effect). Recent methodological advances made in the field of mediation analysis aim at developing statistically reliable estimates of the indirect effect of the treatment on the outcome. However, what appears to be an indirect effect through the mediator may reflect a data generating process without mediation, regardless of the statistical properties of the estimate. To overcome this indeterminacy where possible, we develop the insight that a statistically reliable indirect effect combined with strong evidence for conditional independence of treatment and outcome given the mediator is unequivocal evidence for mediation (as the underlying causal model generating the data) into an operational procedure. Our procedure combines Bayes factors as principled measures of the degree of support for conditional independence, i.e., the degree of support for a Null hypothesis, with latent variable modeling to account for measurement error and discretization in a fully Bayesian framework. We illustrate how our approach facilitates stronger conclusions by re-analzing a set of published mediation studies.

Abstract:

The hypothetical nature of choices collected in typical discrete choice experiments (DCEs) for market research has been a source of concern for both researchers in academia and industry. To the extent that processing the information in choice sets requires effort, classical economic theory questions the external validity of inferences from standard hypothetical (HYP) choices as elicited in market research. Recent studies in marketing indeed demonstrate increased external validity of inferences from choices that are properly incentivized (ICA). However, these studies model the difference between HYP and ICA data collected from the same population as if preferences change. Together, the classical economists’ critique of inference from HYP-DCEs and the notion of changing preferences has led to ignoring the information in HYP data when ICA data are available. In this paper we propose a model that links the information in HYP and ICA data collected in the same population. The model we propose is in the class of sequential-sampling models of choice and assumes that ICA leads respondents to increase their decision effort relative to the standard HYP market research setting, but subject to the same set of “deep” preference parameters. We show that increased amounts of cognitive processing under incentive-alignment materially and plausibly change choice probabilities and outcomes in our model, even if underlying, deep preference parameters are invariant. Our model yields a framework that parsimoniously bridges between data from HYP-DCEs and data from ICA-DCEs that potentially decreases data collection cost at the same level of external predictive validity.

Abstract:

The hypothetical nature of choices collected in typical discrete choice experiments (DCEs) for market research has been a source of concern for both researchers in academia and industry. To the extent that processing the information in choice sets requires effort, classical economic theory questions the external validity of inferences from standard hypothetical (HYP) choices as elicited in market research. Recent studies in marketing indeed demonstrate increased external validity of inferences from choices that are properly incentivized (ICA). However, these studies model the difference between HYP and ICA data collected from the same population as if preferences change. Together, the classical economists’ critique of inference from HYP-DCEs and the notion of changing preferences has led to ignoring the information in HYP data when ICA data are available. In this paper we propose a model that links the information in HYP and ICA data collected in the same population. The model we propose is in the class of sequential-sampling models of choice and assumes that ICA leads respondents to increase their decision effort relative to the standard HYP market research setting, but subject to the same set of “deep” preference parameters. We show that increased amounts of cognitive processing under incentive-alignment materially and plausibly change choice probabilities and outcomes in our model, even if underlying, deep preference parameters are invariant. Our model yields a framework that parsimoniously bridges between data from HYP-DCEs and data from ICA-DCEs that potentially decreases data collection cost at the same level of external predictive validity.

Abstract:

Durables such as cars can often be configured, and equally often, a choice between the financed and non-financed (cash) purchase is possible. Modeling demand in these settings is challenging for several reasons: i) the number of possible combinations, i.e., the size of the implied choice set, is large, ii) the typical configurator combines multinomial choices (e.g., the choice of a car model or engine) with menu choices (optional features that can be freely combined), iii) possible configurations may span enormous price ranges, and iv) configurators for high-ticket items often include financing options. The resulting choice surface is both extremely high-dimensional and highly structured. We extend the model proposed in Kosyakova et al. (2020) to meet these challenges. We construct an exchange-algorithm that handles high-dimensional combinations of multinomial and menu choices that determine the final configuration to infer individual preferences for items and (potentially highly structured) demand interactions. Further, we incorporate liquidity constraints into the model that we again infer without computing the likelihood function, which is prohibitive in all but the smallest configurators. The underlying economic model of choice allows for two liquidity constraints - the maximum cash purchase price and the maximum monthly payment for a financed purchase - possibly constraining the feasible set of choices. A cash purchase requires a higher amount of money upfront explaining choices of financing options. We illustrate our model in a case study that uses configurators in a discrete choice experiment in the car category. We demonstrate implications from ignoring budgetary restrictions and perform counterfactual demand analysis for cash and financing options.

Abstract:

Recent developments in cognitive models in psychology have motivated economics and marketing scholars to adopt these models for economic choice. However, application of cognitive models to economic choice is typically limited to binary choices because of computational difficulties, and generalizing them to larger choice sets is the prerequisite to fully exploit the advantages of these models in empirically interesting discrete choice settings. An example is the dependent Poisson race model (DPRM), a multi-attribute cognitive model with an intractable likelihood for choices

larger than two. In this paper we show how to extend the DPRM to larger choice sets by applying an MCMC based on likelihood approximation. We then propose a massively parallel algorithm that facilitates feasible implemetation of the estimation procedure. The implementation utilizes GPU resources in the Cuda C environment to parallelize likelihood approximation, uses C++ for an efficient execution of loops, and the R environemnt for a user-friendly interface. We discuss the viability of the estimation algorithm and give practical guidelines for an efficient execution of it. Finally, we apply the extended DPRM to a laptop discrete choice experiment data with 4-alternative choice sets, and show that it outperforms the HB logit in out-of-sample predicitions.