Many products and services that are considered in every day choices can be described as mixtures ... more Many products and services that are considered in every day choices can be described as mixtures of ingredients. Examples are the mixture of different fruits composing a fruit salad (e.g. 50% of apples, 30% of wild berries and 20% of grapes) and the mixture of different transportation modes used by an individual on a particular trip (e.g. 70% of travel time by metro and 30% by bike). In some scenarios, the total amount of the mixture may also vary across alternatives. In such cases, the choice between different mixtures depends not only on the proportions but also on the total amount. This type of data is called mixture-amount data. For instance, advertisers have to decide on the advertising media mix in marketing (e.g. 30% of the expenditures on TV advertising, 10% on radio, and 60% on internet) as well as on the total budget of the entire campaign. The mix of transportation modes chosen by a traveler may also depend on the total travel time. In other scenarios, the choice of a mix...
This article examines the global spillover of foreign product introductions and takeoffs on a foc... more This article examines the global spillover of foreign product introductions and takeoffs on a focal country's time to takeoff, using a novel data set of penetration data for eight high-tech products across 55 countries. It shows how foreign clout, the susceptibility to foreign influences, and intercountry distances affect global spillover patterns. The authors find that foreign takeoffs, but not foreign introductions, accelerate a focal country's time to takeoff. The larger the country, the higher its economic wealth, and the more it exports, the more clout it has in the global spillover process. In contrast, the poorer the country, the more tourists it receives, and the higher its population density, the more susceptible it is to global spillover effects. Cross-country spillover effects are stronger the closer the countries are to one another, both geographically and economically, but not necessarily in terms of culture. The model the authors develop also quantifies the spi...
In this chapter we use a simulation experiment to examine whether the seasonal adjustment methods... more In this chapter we use a simulation experiment to examine whether the seasonal adjustment methods Census X12-ARIMA and TRAMO/SEATS effectively remove seasonality properties from time series data, while preserving other features like the stochastic trend. As data generating processes we use a variety of processes that are actually found in practice. These processes include constant seasonality, changing seasonal patterns due to seasonal unit roots and processes with periodically varying parameters. To check for seasonality, we consider tests for seasonal unit roots, for deterministic seasonality, for seasonality in the variance, and for periodicity in the parameters. Our simulation results show that both adjustment methods are able to remove stochastic seasonal patterns from the data with the exception of changing seasonal patterns due to periodicity in the parameters. On average, the two methods perform equally well.
We introduce a multi-level smooth transition model for a panel of time series variables, which ca... more We introduce a multi-level smooth transition model for a panel of time series variables, which can be used to examine the presence of common non-linear features across many such variables. The model is positioned in between a fully pooled model, which imposes such common features, and a fully heterogeneous model, which might render estimation problems for some of the panel members. To keep the model tractable, we introduce a second-stage model, which links the parameters in the transition functions with observable explanatory variables. We discuss representation, estimation by concentrated simulated maximum likelihood and inference. We illustrate our model for data on industrial production of 18 US manufacturing sectors, and document that there are subtle differences across sectors in leads and lags for business cycle recessions and expansions.
To comprehend the competitive structure of a market, it is important to understand the short-run ... more To comprehend the competitive structure of a market, it is important to understand the short-run and long-run effects of the marketing mix on market shares. A useful model to link market shares with marketing-mix variables, like price and promotion, is the market share attraction model. In this paper we put forward a representation of the attraction model, which allows for explicitly disentangling long-run from short-run effects. Our model also contains a second level, in which these dynamic effects are correlated with various brand and product category characteristics. Based on the findings in for example Nijs et al. (2001), we postulate the expected signs of these correlations. We fit our resultant Hierarchical Bayes attraction model to data on seven categories in two geographical areas. This data set spans a total of 50 brands. Our main finding is that, in absolute sense, the short-run price elasticity usually exceeds the long-run effect. Moreover, we find that the longrun price ...
To examine cross-country diffusion of new products, marketing researchers have to rely on a multi... more To examine cross-country diffusion of new products, marketing researchers have to rely on a multivariate product growth model. We put forward such a model, and show that it is a natural extension of the original Bass (1969) model. We contrast our model with currently in use multivariate models and we show that inference is much easier and interpretation is straightforward. Especially if the number of countries is larger than two. In fact, parameter estimation can be done using standard commercially available software. We illustrate the benefits of our model relative to other models in simulation experiments. These experiments show that in the competing models the cross-country effects are actually very difficult to identify from the data. An application to a three-country CD sales series shows the merits of our model in practice.
Sales models are mainly used to analyze markets with a fairly small number of items, obtained aft... more Sales models are mainly used to analyze markets with a fairly small number of items, obtained after aggregating to the brand level. In practice one may require analyses at a more disaggregate level. For example, brand managers may be interested in a comparison across product attributes. For such an analysis the number of relevant items in the product category make commonly used sales models difficult to use as they would contain too many parameters. In this paper we propose a new model, which allows for the analysis of a market with many items while using only a moderate number of easily interpretable parameters. This is achieved by writing the sales model as a Hierarchical Bayes model. In this way we relate the marketing-mix effectiveness to item characteristics such as brand, package size, package type and shelf position. In this specification we do not have to impose restrictions on the competitive structure, as all items are allowed to have different own and cross elasticities. ...
This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These... more This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase fr...
By using smooth effect for predictors, a researcher is relieved of the burden of assuming a speci... more By using smooth effect for predictors, a researcher is relieved of the burden of assuming a specific functional form for how a predictor influences the response variable. For a data set with many predictors, estimation of smooth effects might become difficult computationally, and overfitting might occur. Our research overcomes these issues by using the Spike and Slab Generalized Additive Model (SSGAM) proposed by Scheipl et al. (2012). This Bayesian method estimates smooth effects, including interaction effects, and shrinks small effects to prevent overfitting. The contribution of our paper is to make this methodology feasible for a data set with many predictors. We propose to apply a first step of variable selection with DART proposed by Linero (2018), which performs variable selection with a Bayesian modification of a decision tree ensemble. In this way, we can estimate smooth effects for a data sets with many predictors. Our proposed methodology is used to model the choice of vie...
Screening for diseases is common practice in illness detection. The design of optimal, personaliz... more Screening for diseases is common practice in illness detection. The design of optimal, personalized screening intervals has received more attention as personalized medicine has become more popular. In this work, we focus on the modeling of longitudinal biomarker measurements. We extend the framework of joint modeling in the eld of screening intervals of Rizopoulos et al. (2016) in two directions. First, we consider a Bayesian model average specication. Second, we allow for the simultaneous scheduling of multiple screenings. We illustrate the use of our adaptions with an application among heart failure patients and the NT-proBNP biomarker. We nd that (i) higher levels of the biomarker places the patient at greater risk for cardiac events and (ii) that Bayesian model averaging allows for modeling non-standard biomarker trajectories.
Many products and services that are considered in every day choices can be described as mixtures ... more Many products and services that are considered in every day choices can be described as mixtures of ingredients. Examples are the mixture of different fruits composing a fruit salad (e.g. 50% of apples, 30% of wild berries and 20% of grapes) and the mixture of different transportation modes used by an individual on a particular trip (e.g. 70% of travel time by metro and 30% by bike). In some scenarios, the total amount of the mixture may also vary across alternatives. In such cases, the choice between different mixtures depends not only on the proportions but also on the total amount. This type of data is called mixture-amount data. For instance, advertisers have to decide on the advertising media mix in marketing (e.g. 30% of the expenditures on TV advertising, 10% on radio, and 60% on internet) as well as on the total budget of the entire campaign. The mix of transportation modes chosen by a traveler may also depend on the total travel time. In other scenarios, the choice of a mix...
This article examines the global spillover of foreign product introductions and takeoffs on a foc... more This article examines the global spillover of foreign product introductions and takeoffs on a focal country's time to takeoff, using a novel data set of penetration data for eight high-tech products across 55 countries. It shows how foreign clout, the susceptibility to foreign influences, and intercountry distances affect global spillover patterns. The authors find that foreign takeoffs, but not foreign introductions, accelerate a focal country's time to takeoff. The larger the country, the higher its economic wealth, and the more it exports, the more clout it has in the global spillover process. In contrast, the poorer the country, the more tourists it receives, and the higher its population density, the more susceptible it is to global spillover effects. Cross-country spillover effects are stronger the closer the countries are to one another, both geographically and economically, but not necessarily in terms of culture. The model the authors develop also quantifies the spi...
In this chapter we use a simulation experiment to examine whether the seasonal adjustment methods... more In this chapter we use a simulation experiment to examine whether the seasonal adjustment methods Census X12-ARIMA and TRAMO/SEATS effectively remove seasonality properties from time series data, while preserving other features like the stochastic trend. As data generating processes we use a variety of processes that are actually found in practice. These processes include constant seasonality, changing seasonal patterns due to seasonal unit roots and processes with periodically varying parameters. To check for seasonality, we consider tests for seasonal unit roots, for deterministic seasonality, for seasonality in the variance, and for periodicity in the parameters. Our simulation results show that both adjustment methods are able to remove stochastic seasonal patterns from the data with the exception of changing seasonal patterns due to periodicity in the parameters. On average, the two methods perform equally well.
We introduce a multi-level smooth transition model for a panel of time series variables, which ca... more We introduce a multi-level smooth transition model for a panel of time series variables, which can be used to examine the presence of common non-linear features across many such variables. The model is positioned in between a fully pooled model, which imposes such common features, and a fully heterogeneous model, which might render estimation problems for some of the panel members. To keep the model tractable, we introduce a second-stage model, which links the parameters in the transition functions with observable explanatory variables. We discuss representation, estimation by concentrated simulated maximum likelihood and inference. We illustrate our model for data on industrial production of 18 US manufacturing sectors, and document that there are subtle differences across sectors in leads and lags for business cycle recessions and expansions.
To comprehend the competitive structure of a market, it is important to understand the short-run ... more To comprehend the competitive structure of a market, it is important to understand the short-run and long-run effects of the marketing mix on market shares. A useful model to link market shares with marketing-mix variables, like price and promotion, is the market share attraction model. In this paper we put forward a representation of the attraction model, which allows for explicitly disentangling long-run from short-run effects. Our model also contains a second level, in which these dynamic effects are correlated with various brand and product category characteristics. Based on the findings in for example Nijs et al. (2001), we postulate the expected signs of these correlations. We fit our resultant Hierarchical Bayes attraction model to data on seven categories in two geographical areas. This data set spans a total of 50 brands. Our main finding is that, in absolute sense, the short-run price elasticity usually exceeds the long-run effect. Moreover, we find that the longrun price ...
To examine cross-country diffusion of new products, marketing researchers have to rely on a multi... more To examine cross-country diffusion of new products, marketing researchers have to rely on a multivariate product growth model. We put forward such a model, and show that it is a natural extension of the original Bass (1969) model. We contrast our model with currently in use multivariate models and we show that inference is much easier and interpretation is straightforward. Especially if the number of countries is larger than two. In fact, parameter estimation can be done using standard commercially available software. We illustrate the benefits of our model relative to other models in simulation experiments. These experiments show that in the competing models the cross-country effects are actually very difficult to identify from the data. An application to a three-country CD sales series shows the merits of our model in practice.
Sales models are mainly used to analyze markets with a fairly small number of items, obtained aft... more Sales models are mainly used to analyze markets with a fairly small number of items, obtained after aggregating to the brand level. In practice one may require analyses at a more disaggregate level. For example, brand managers may be interested in a comparison across product attributes. For such an analysis the number of relevant items in the product category make commonly used sales models difficult to use as they would contain too many parameters. In this paper we propose a new model, which allows for the analysis of a market with many items while using only a moderate number of easily interpretable parameters. This is achieved by writing the sales model as a Hierarchical Bayes model. In this way we relate the marketing-mix effectiveness to item characteristics such as brand, package size, package type and shelf position. In this specification we do not have to impose restrictions on the competitive structure, as all items are allowed to have different own and cross elasticities. ...
This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These... more This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase fr...
By using smooth effect for predictors, a researcher is relieved of the burden of assuming a speci... more By using smooth effect for predictors, a researcher is relieved of the burden of assuming a specific functional form for how a predictor influences the response variable. For a data set with many predictors, estimation of smooth effects might become difficult computationally, and overfitting might occur. Our research overcomes these issues by using the Spike and Slab Generalized Additive Model (SSGAM) proposed by Scheipl et al. (2012). This Bayesian method estimates smooth effects, including interaction effects, and shrinks small effects to prevent overfitting. The contribution of our paper is to make this methodology feasible for a data set with many predictors. We propose to apply a first step of variable selection with DART proposed by Linero (2018), which performs variable selection with a Bayesian modification of a decision tree ensemble. In this way, we can estimate smooth effects for a data sets with many predictors. Our proposed methodology is used to model the choice of vie...
Screening for diseases is common practice in illness detection. The design of optimal, personaliz... more Screening for diseases is common practice in illness detection. The design of optimal, personalized screening intervals has received more attention as personalized medicine has become more popular. In this work, we focus on the modeling of longitudinal biomarker measurements. We extend the framework of joint modeling in the eld of screening intervals of Rizopoulos et al. (2016) in two directions. First, we consider a Bayesian model average specication. Second, we allow for the simultaneous scheduling of multiple screenings. We illustrate the use of our adaptions with an application among heart failure patients and the NT-proBNP biomarker. We nd that (i) higher levels of the biomarker places the patient at greater risk for cardiac events and (ii) that Bayesian model averaging allows for modeling non-standard biomarker trajectories.
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Papers by D. Fok