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Analysts fitting a hierarchical Bayesian model must specify the distribution of heterogeneity. There are several distributions to choose from, including the multivariate normal, mixture of normals, Dirichlet processes priors, and so forth. Although significant progress has been made, estimating the models and obtaining measures for model selection remain ongoing areas of research for more flexible distributions of heterogeneity. As a result, the multivariate normal remains the default choice for many researchers and software packages. This article proposes model-checking statistics that signal the adequacy of the multivariate normal assumption for the distribution of heterogeneity; these methods do not require the analyst to fit alternative models. The authors use posterior predictive model checking to determine whether a discrepancy exists between the individual-level parameters and those implied by the assumed distribution of heterogeneity. In simulated and real data sets, the results show that these statistics are useful for identifying when the multivariate normal distribution is adequate, when there is a departure in the tails of the distribution, and when a multimodal distribution of heterogeneity may be more appropriate.

The majority of brand extensions reportedly fail, suggesting the need for methodologies that allow for better strategic prediction of categories into which a brand should extend or license. Prior literature suggests that brand extensions are likely to be more successful if a brand extends into another category into which its existing brand associations and imagery “fit” better and if the extending brand is “atypical” (if it possesses associations and imagery that are broad and abstract rather than tied too closely to the brand's original product category). The authors develop a methodology in this study to estimate brand and category personality structures, using a Bayesian factor model that separates the two by means of brand-level and category-level random effects. This methodology leads to measures of a brand's fit and atypicality. The authors illustrate and validate the model on two nationally representative data sets on brand personalities in three categories (jeans, magazines, and cars) and investigate the brand extension and licensing implications of the results obtained with the model.

Marketers often analyze multinomial choice from a set of branded products to learn about demand. Given a set of brands to study, we analyze three reasons why choices from strict subsets of the brands can contain more statistical information about demand than choices from all the brands in the study. First, making choices from smaller subsets is easier, so it is possible to use more choice-tasks when the choice data comes from a choice-based conjoint questionnaire. Second, choices from subsets of brands better identify and more accurately estimate the covariance structure of unobserved utility shocks associated with brands. Third, subsets automatically balance the brand-shares when some of the brands are less popular than others. We demonstrate these three "benefits of subsets" using a mixture of analytical results and numerical simulations, and provide implications for the design of choice-based conjoint analyses. We find that the optimal subset-size depends on the model, the number of brands in the study, and the designer's resource constraint. Besides showing that subsets can be beneficial, we also provide a simulation methodology that helps designers pick the best subset-size for their setting.

Informative priors that reflect the structure of the model can improve estimation when data are sparse, while “standard,” noninformative priors can have unintended consequences. First, the authors discuss selecting informative priors for variances and introduce a conjugate prior for covariance matrices. The proposed prior is more flexible than the inverse Wishart without increasing computations. Second, the authors investigate the impact of priors for the covariance of parameter heterogeneity when the predictor variables are qualitative. Estimates of the omitted effects are spurious with the standard prior. The authors propose an effects prior that treats all effects symmetrically. Third, the authors consider willingness to pay. These ratio estimators magnify uncertainty in the price coefficients and can give unreasonable values for price-insensitive consumers. The authors show that estimation of willingness to pay can be greatly improved by restricting the parameters without distorting them. In ...

Planning and evaluating consumer promotions is facilitated by knowledge of the types of consumers who contribute to incremental sales. In particular, interest may focus on identifying the contributions of buyers segmented on the basis of their prior purchase history. When the distribution of the number of purchase occasions in a base period can be described by the negative binomial distribution (NBD), conditional trend analysis (CTA) is a simple and effective approach for identifying the sources of incremental sales during a test (promotional) period. As currently implemented, CTA assumes a stationary marketing environment. The authors propose an extension of CTA that explicitly incorporates varying marketing activities. They also show that the often observed underprediction of purchases in the test period by nonbuyers in the base period is a consequence of the skewness of the NBD and is not necessarily due to model misspecification. An illustration with scanner panel data is provided.