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, p (coefficient of innovation), q (coefficient of imitation), and c (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 p and c decrease and those of q increase when data exhibit more right skew than the Bass model and (2) the estimates of p and c 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 q/p, (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 c increase and those of q decrease for both the Bass and the G/SG models. The estimates of p increase as one adds data points only for the G/SG model. No significant tendency in parameter estimates of p 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".

A maximum likelihood approach is proposed for estimating an innovation diffusion model of new product acceptance originally considered by Bass (Bass, F. M. 1969. A new product growth model for consumer durables. Management Sci. 15 (January) 215–227.). The suggested approach allows: (1) computation of approximate standard errors for the diffusion model parameters, and (2) determination of the required sample size for forecasting the adoption level to any desired degree of accuracy. Using histograms from eight different product innovations, the maximum likelihood estimates are shown to outperform estimates from a model calibrated using ordinary least squares, in terms of both goodness of fit measures and one-step ahead forecasts. However, these advantages are not obtained without cost. The coefficients of innovation and imitation are easily interpreted in terms of the expected adoption pattern, but individual adoption times must be assumed to represent independent draws from this distribution. In addition, instead of using standard linear regression, another (simple) program must be employed to estimate the model. Thus, tradeoffs between the maximum likelihood and least squares approaches are also discussed.

We provide a fully personalized model for optimizing multiple marketing interventions in intermediate-term customer relationship management (CRM). We derive theoretically based propositions on the moderating effects of past customer behavior and conduct a longitudinal validation test to compare the performance of our model with that of commonly used segmentation models in predicting intermediate-term, customer-specific gross profit change. Our findings show that response to marketing interventions is highly heterogeneous, that heterogeneity of response varies across different marketing interventions, and that the heterogeneity of response to marketing interventions may be partially explained by customer-specific variables related to customer characteristics and the customer’s past interactions with the company. One important result from these moderating effects is that relationship-oriented interventions are more effective with loyal customers, while action-oriented interventions are more effective with nonloyal customers. We show that our proposed model outperformed models based on demographics, recency-frequency-monetary value (RFM), or finite mixture segmentation in predicting the effectiveness of intermediate-term CRM. The empirical results project a significant increase in intermediate-term profitability over all of the competing segmentation approaches and a significant increase in intermediate-term profitability over current practice.

Customer base analysis is concerned with using the observed past purchase behavior of customers to understand their current and likely future purchase patterns. More specifically, as developed in Schmittlein et al. (1987), customer base analysis uses data on the frequency, timing, and dollar value of each customer's past purchases to infer • the number of customers currently active, • how that number has changed over time, • which individual customers are most likely still active, • how much longer each is likely to remain an active customer, and • how many purchases can be expected from each during any future time period of interest. In this paper we empirically validate the model proposed by Schmittlein et al. In doing so, we provide one of the few applications of stochastic models to industrial purchase processes and industrial marketing decisions. Besides showing that the model does capture key aspects of the purchase process, we also present a more effective parameter estimation method and some results regarding sampling properties of the parameter estimates. Finally, we extend the model to explicitly incorporate dollar volume of past purchases. Our results indicate that this kind of customer base analysis can be both effective in predicting purchase patterns and in generating insights into how key customer groups differ. The link of both these benefits to industrial marketing decision making is also discussed.

Amultinomial logit model of brand choice, calibrated on 32 weeks of purchases of regular ground coffee by 100 households, shows high statistical significance for the explanatory variables of brand loyalty, size loyalty, presence/absence of store promotion, regular shelf price and promotional price cut. The model is parsimonious in that the coefficients of these variables are modeled to be the same for all coffee brand-sizes. The calibrated model predicts remarkably well the share of purchases by brand-size in a hold-out sample of 100 households over the 32-week calibration period and a subsequent 20-week forecast period. The success of the model is attributed in part to the level of detail and completeness of the household panel data employed, which has been collected through optical scanning of the Universal Product Code in supermarkets. Three short-term market response measures are calculated from the model: regular (depromoted) price elasticity of share, percent increase in share for a promotion with a median price cut, and promotional price cut elasticity of share. Response varies across brand-sizes in a systematic way with large share brand-sizes showing less response in percentage terms but greater in absolute terms. On the basis of the model a quantitative picture emerges of groups of loyal customers who are relatively insensitive to marketing actions and a pool of switchers who are quite sensitive. This article was originally published in Marketing Science, Volume 2, Issue 3, pages 203–238, in 1983.

Over a large number of new products and technological innovations, the Bass diffusion model (Bass 1969) describes the empirical adoption curve quite well. In this study, we generalize the Bass model to include decision variables such as price and advertising. The generalized model reduces to the Bass model as a special case and explains why the Bass model works so well without including decision variables. We compare our generalized Bass model to other approaches from the literature for including decision variables into diffusion models, and our results provide both theoretical and empirical support for the generalized Bass model. We also show how our generalized Bass model can be used for product planning purposes.

We estimate the causal effects of different targeted email promotions on the opening and purchase decisions of the consumers who receive them.