Peter Lenk

Modeling Household Purchase Behavior with Logistic Normal Regression

The successful development of marketing strategies requires the accurate measurement of household preferences and their reaction to variables such as price and advertising. Manufacturers, for examp...

Bayesian Inference for Finite Mixtures of Generalized Linear Models with Random Effects.

We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.

Discrete and Continuous Representations of Unobserved Heterogeneity in Choice Modeling

We attempt to provide insights into how heterogeneity has been and can be addressed in choice modeling. In doing so, we deal with three topics: Models of heterogeneity, Methods of estimation and Substantive issues. In describing models we focus on discrete versus continuous representations of heterogeneity. With respect to estimation we contrast Markov Chain Monte Carlo methods and (simulated) likelihood methods. The substantive issues discussed deal with empirical tests of heterogeneity assumptions, the formation of empirical generalisations, the confounding of heterogeneity with state dependence and consideration sets, and normative segmentation.

Reassessing Brand Loyalty, Price Sensitivity, and Merchandising Effects on Consumer Brand Choice

This article reports the results of an empirical study of household brand choices over four scanner-panel data sets. The study uses a random-effects, autocorrelated, logistic regression model. The analysis presents evidence that the brand-choice process is not zero-order. In addition, the influence of in-store displays and feature advertisements on switching is shown to be about two to three times more effective than estimates obtained from previous studies. Finally, the analysis indicates systematic differences between frequent and infrequent buyers of products in terms of their sensitivity to price, displays, and feature advertising.

Brand extension strategy planning: Empirical estimation of brand-category personality fit and atypicality

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 brands 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 brands 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.

Bayesian inference for semiparametric regression using a Fourier representation

This paper presents the Bayesian analysis of a semiparametric regression model that consists of parametric and nonparametric components. The nonparametric component is represented with a Fourier series where the Fourier coefficients are assumed a priori to have zero means and to decay to 0 in probability at either algebraic or geometric rates. The rate of decay controls the smoothness of the response function. The posterior analysis automatically selects the amount of smoothing that is coherent with the model and data. Posterior probabilities of the parametric and semiparametric models provide a method for testing the parametric model against a non‐specific alternative. The Bayes estimator’s mean integrated squared error compares favourably with the theoretically optimal estimator for kernel regression.

A Utility Theoretic Examination of the Probability Ranking Principle in Information Retrieval.

We challenge the probability ranking principle in information retrieval from the perspectives of (1) signal detection‐decision theory and (2) utility theory. If three conditions are not met by an IR system that is producing predictive probabilities of relevance, then inquirers may incur costs that are too great by selecting first those documents that the system predicts have the highest probabilities of relevance. These three conditions are that predictive probabilities are well calibrated (predictively accurate); that they are reported with certainty; and that an inquirer independently assesses the relevance of all documents he or she retrieves. When these conditions are met, signal detection analysis with fixed decision‐theoretic costs shows that the probability ranking principle is advisable. More generally, retrieval in adherence with the probability ranking principle is also advisable even when utility‐theoretic costs (or benefits) that vary with the number of relevant documents retrieved are associated with retrieval. Specifically, we prove that the utility an inquirer receives from the relevant documents he or she retrieves is maximized by selecting those documents with the largest predictive probabilities of relevance.

Representing Heterogeneity in Consumer Response Models 1996 Choice Conference Participants

We define sources of heterogeneity in consumer utility functions relatedto individual differences in response tendencies, drivers of utility, formof the consumer utility function, perceptions of attributes, statedependencies, and stochasticity. A variety of alternative modelingapproaches are reviewed that accommodate subsets of these various sourcesincluding clusterwise regression, latent structure models, compounddistributions, random coefficients models, etc. We conclude by defining anumber of promising research areas in this field.

When is the probability ranking principle suboptimal

The probability ranking principle retrieves documents in decreasing order of their predictive probabilities of relevance. Gordon and Lenk (1991) demonstrated that this principal is optimal within a signal detection—decision theory framework, and it maximizes the inquirers expected utility for relevant documents. These results hold under three conditions: calibration, independent assessment of relevance by the inquirer, and certainty about the computed probabilities of relevance. We demonstrate that the probability ranking principle can be suboptimal with respect to expected utility when one of these conditions fails to hold.

On Priors With a Kullback-Leibler Property

In this paper, we highlight properties of Bayesian models in which the prior puts positive mass on all Kullback–Leibler neighborhoods of all densities. These properties are concerned with model choice via the Bayes factor, density estimation and the maximization of expected utility for decision problems. In four illustrations we focus on the Bayes factor and show that whatever models are being compared, the [log(Bayes factor)]/[sample size] converges to a non-random number which has a nice interpretation. A parametric versus semiparametric model comparison provides a fifth illustration.