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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46977/1/11002_2004_Article_230988.pd

Statistical Analysis of Choice Experiments and Surveys

Measures of households' past behavior, their expectations with respect to future events and contingencies, and their intentions with respect to future behavior are frequently collected using household surveys. These questions are conceptually difficult. Answering them requires elaborate cognitive and social processes, and often respondents report only their “best” guesses and/or estimates, using more or less sophisticated heuristics. A large body of literature in psychology and survey research shows that as a result, responses to such questions may be severely biased. In this paper, (1) we describe some of the problems that are typically encountered, (2) provide some empirical illustrations of these biases, and (3) develop a framework for conceptualizing survey response behavior and for integrating structural models of response behavior into the statistical analysis of the underlying economic behavior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47001/1/11002_2005_Article_5884.pd

Stochastic modeling of consumer purchase behavior : I. Analytical Results

This paper develops alternative brand purchase models. These models are based on distinct assumptions about the product class purchasing process over a fixed time-period. In each case, the brand choice process conditioned on a product purchase being made is assumed to be heterogeneous zero order. New analytical closed-form results are derived. These results include various market statistics such as the brand penetration, the mean and variance of the brand purchase distribution and the aggregate brand purchase distribution itself. These theoretical expressions are based on the assumption of independence between brand choice probability and mean product purchase rate across the population

Statistical Analysis of Choice Experiments and Surveys

Abstract: Measures of households ’ past behavior, their expectations with respect to future events and contingencies, and their intentions with respect to future behavior are frequently collected using household surveys. These questions are conceptually difficult. Answering them requires elaborate cognitive and social processes, and often respondents report only their “best” guesses and/or estimates, using more or less sophisticated heuristics. A large body of literature in psychology and survey research shows that as a result, responses to such questions may be severely biased. In this paper, (1) we describe some of the problems that are typically encountered, (2) provide some empirical illustrations of these biases, and (3) develop a framework for conceptualizing survey response behavior and for integrating structural models of response behavior into the statistical analysis of the underlying economic behavior

The Impact of Heterogeneity and Ill-Conditioning on Diffusion Model Parameter Estimates

Assessment of accurate market size and early adoption patterns is essential to strategic decision making of managers involved in new-product launches. This article proposes methodology that explains changes in parameter estimates of the Bass model, (coefficient of innovation), (coefficient of imitation), and (market penetration rate) by direction of "extra-Bass" skew in the data, or equivalently, by underlying heterogeneity of the population. This research shows significantly opposite patterns of these parameter estimates, depending on skew of the diffusion curve detected by a generalized model, i.e., the gamma/shifted Gompertz (G/SG) model, which embeds the Bass model as a special case. The G/SG model originally presented in Bemmaor (1994) is based on two assumptions: (1) Individual-level times to first purchase are distributed shifted Gompertz and (2) individual-level propensity to buy follows a gamma distribution across the population. We assume that the scale parameter of the shifted Gompertz distribution is constant across consumers. The advantage the G/SG model has over alternative diffusion models such as the nonuniform influence model is that its cumulative distribution function takes a closed-form expression. In line with Van den Bulte and Lilien (1997), we analyze these opposite patterns from simulated data using the G/SG model as the true model and 12 real adoption data sets. The patterns are: (1) as the level of censoring decreases, the estimates of and decrease and those of increase when data exhibit more right skew than the Bass model and (2) the estimates of and increase and those of q decrease when data exhibit more left skew than the Bass model. For the simulated data, we manipulated four dimensions: (1) "extra-Bass" skew in the data, (2) ratio , (3) speed of diffusion, and (4) error variance. Both results of the simulated data and the real adoption data sets confirm the existence of two opposite patterns of parameter estimates of the Bass model depending on "extra-Bass" skew. When the model is correctly specified with simulated data, estimates of increase and those of decrease for both the Bass and the G/SG models. The estimates of increase as one adds data points only for the G/SG model. No significant tendency in parameter estimates of was detected for the Bass model. As for ill-conditioning issues, systematic changes in the parameter estimates of the G/SG model can be substantially larger in some cases than those obtained with the Bass model, even though the data were generated by taking the G/SG model as the true one. Therefore, model complexity can aggravate the tendency for parameters to change systematically as one adds data points. The forecasting results from the simulated data show the supremacy of the G/SG model. It provides more accurate results than the Bass model in the one-step ahead, two-step ahead, and three-step ahead forecasts. With the real data set, the G/SG model provides more accurate one-step ahead forecasts than the Bass model, but the model's forecasting performance deteriorates more rapidly than the Bass model when one shifts to two-step ahead and three-step ahead forecasts. The systematic changes in parameter estimates are larger for the more complex model. Our research shows that the G/SG model is a flexible model used to analyze the systematic changes in parameter estimates when specification error and ill-conditioning occur. As our findings incorporate two possible types of parameter estimate bias, compared to the previous single-direction view, they can provide essential information to enhance forecasting accuracy of products and services using new technological innovations. Our forecasting results of simulated and real adoption data raise a question about the optimal horizon of forecasting in applying flexible models of diffusion. The G/SG model also provides grounds to investigate jointly "the speed of takeoff" and "the diffusion speed after takeoff".Diffusion, New-Product Diffusion, Forecasting