Semiparametric analysis to estimate the deal effect curve

The marketing literature suggests several phenomena that may contribute to the shape of the relationship between sales and price discounts. These phenomena can produce severe nonlinearities and interactions in the curves, and we argue that those are best captured with a flexible approach. Since a fully nonparametric regression model suffers from the curse of dimensionality, we propose a semiparametric regression model. Store-level sales over time is modeled as a nonparametric function of own-and cross-item price discounts, and a parametric function of other predictors (all indicator variables). We compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain better performance on average. The results for three product categories indicate a.o. threshold- and saturation effects for both own- and cross-item temporary price cuts. We also show how the own-item curve depends on other items’ price discounts (flexible interaction effects). In a separate analysis, we show how the shape of the deal effect curve depends on own-item promotion signals. Our results indicate that prevailing methods for the estimation of deal effects on sales are inadequate.

Consideration sets, intentions and the inclusion of "Don't know" in a two-stage model for voter choice

We present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage. The first stageinvolves a multivariate probit model for the vector of probabilities that a candidate or a party gets considered. The second stage of the model is a multinomial probit model for the actual choice. In both stages we use asexplanatory variables data on voter choice at the previous election, as well as socio-demographic respondent characteristics. Importantly, our modelexplicitly accounts for the three types of "missing data" encountered in polling. First, we include a no-vote option in the final vote intention stage. Second, the "do not know" response is assumed to arise from too little difference in the utility between the two most preferred options in the consideration set. Third, the "do not want to say" response is modelled as a missing observation on the most preferred alternative in the consideration set. Thus, we consider the missing data generating mechanism to be non-ignorable and build a model based on utility maximization to describe the voting intentions of these respondents. We illustrate the merits of the model as we have information on a sample of about 5000 individuals from the Netherlands for who we know how they voted last time (if at all), which parties they would consider for the upcoming election,and what their voting intention is. A unique feature of the data set is that information is available on actual individual voting behavior, measured at the day of election. We find that the inclusion of the consideration set stage in the model enables the user to make more precise inferences on the competitive structure in the political domain and to get better out-of-sample forecasts.Bayesian method;Choice model;Election data;Polling;Probit model

How Promotions Work: SCAN*PRO-Based Evolutionary Model Building

We provide a rationale for evolutionary model building. The basic idea is that to enhance user acceptance it is important that one begins with a relatively simple model. Simplicity is desired so that managers understand models. As a manager uses the model and builds up experience with this decision aid, she will realize its shortcomings. The model will then be expanded and will lead to the increase of complexity. Evolutionary model building also stimulates the generalization of marketing knowledge. We illustrate this by discussing different extensions of the SCAN*PRO model. The purpose of published model extensions is to increase the knowledge about "how promotions work" and to provide support for more complex decisions. We summarize the generated knowledge about how promotions work, based on this process.We provide a rationale for evolutionary model building. The basic idea is that to enhance user acceptance it is important that one begins with a relatively simple model. Simplicity is desired so that managers understand models. As a manager uses the model and builds up experience with this decision aid, she will realize its shortcomings. The model will then be expanded and will lead to the increase of complexity. Evolutionary model building also stimulates the generalization of marketing knowledge. We illustrate this by discussing different extensions of the SCAN*PRO model. The purpose of published model extensions is to increase the knowledge about "how promotions work" and to provide support for more complex decisions. We summarize the generated knowledge about how promotions work, based on this process.Articles published in or submitted to a Journal without I

Semiparametric analysis to estimate the deal effect curve

The marketing literature suggests several phenomena that may contribute to the shape of the relationship between sales and price discounts. These phenomena can produce severe nonlinearities and interactions in the curves, and we argue that those are best captured with a flexible approach. Since a fully nonparametric regression model suffers from the curse of dimensionality, we propose a semiparametric regression model. Store-level sales over time is modeled as a nonparametric function of own-and cross-item price discounts, and a parametric function of other predictors (all indicator variables). We compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain better performance on average. The results for three product categories indicate a.o. threshold- and saturation effects for both own- and cross-item temporary price cuts. We also show how the own-item curve depends on other items’ price discounts (flexible interaction effects). In a separate analysis, we show how the shape of the deal effect curve depends on own-item promotion signals. Our results indicate that prevailing methods for the estimation of deal effects on sales are inadequate

The estimation of pre- and postpromotion dips with store-level scanner data

One of the mysteries of store-level scanner data modeling is the lack of a dip in sales in the week(s) following a promotion. Researchers expect to find a postpromotion dip because analyses of household scanner panel data indicate that consumers tend to accelerate their purchases in response to a promotion that is, they buy earlier and/or purchase larger quantities than they would in the absence of a promotion. Thus, one should also find a pronounced dip in store-level sales in the week(s) following a promotion. However, researchers find such dips usually neither at the category nor at the brand level. Several arguments have been proposed for the lack of a postpromotion dip in store-level sales data. These arguments explain why dips may be hidden. Given that dips are difficult to detect by traditional models (and by a visual inspection of the data), we propose models that can account for a multitude of factors which together cause complex pre- and postpromotion dips. We use three alternative distributed lead- and lag structures: an Almon model, an Unrestricted dynamic effects model, and an Exponential decay model. In each model, we include four types of price discounts: without any support, with display-only support, with feature-only support, and with feature and display support. The models are calibrated on store-level scanner data for two product categories: tuna and toilet tissue. We estimate the dip to be between 4 and 25 percent of the current sales effect, which is consistent with household-level studies

Imposed work of breathing during high-frequency oscillatory ventilation: a bench study

INTRODUCTION: The ventilator and the endotracheal tube impose additional workload in mechanically ventilated patients breathing spontaneously. The total work of breathing (WOB) includes elastic and resistive work. In a bench test we assessed the imposed WOB using 3100 A/3100 B SensorMedics high-frequency oscillatory ventilators. METHODS: A computer-controlled piston-driven test lung was used to simulate a spontaneously breathing patient. The test lung was connected to a high-frequency oscillatory ventilation (HFOV) ventilator by an endotracheal tube. The inspiratory and expiratory airway flows and pressures at various places were sampled. The spontaneous breath rate and volume, tube size and ventilator settings were simulated as representative of the newborn to adult range. The fresh gas flow rate was set at a low and a high level. The imposed WOB was calculated using the Campbell diagram. RESULTS: In the simulations for newborns (assumed body weight 3.5 kg) and infants (assumed body weight 10 kg) the imposed WOB (mean ± standard deviation) was 0.22 ± 0.07 and 0.87 ± 0.25 J/l, respectively. Comparison of the imposed WOB in low and high fresh gas flow rate measurements yielded values of 1.63 ± 0.32 and 0.96 ± 0.24 J/l (P = 0.01) in small children (assumed body weight 25 kg), of 1.81 ± 0.30 and 1.10 ± 0.27 J/l (P < 0.001) in large children (assumed body weight 40 kg), and of 1.95 ± 0.31 and 1.12 ± 0.34 J/l (P < 0.01) in adults (assumed body weight 70 kg). High peak inspiratory flow and low fresh gas flow rate significantly increased the imposed WOB. Mean airway pressure in the breathing circuit decreased dramatically during spontaneous breathing, most markedly at the low fresh gas flow rate. This led to ventilator shut-off when the inspiratory flow exceeded the fresh gas flow. CONCLUSION: Spontaneous breathing during HFOV resulted in considerable imposed WOB in pediatric and adult simulations, explaining the discomfort seen in those patients breathing spontaneously during HFOV. The level of imposed WOB was lower in the newborn and infant simulations, explaining why these patients tolerate spontaneous breathing during HFOV well. A high fresh gas flow rate reduced the imposed WOB. These findings suggest the need for a demand flow system based on patient need allowing spontaneous breathing during HFOV