One of the most important issues for direct marketers is how to sample targets from a population for a direct marketing campaign. Many authors have proposed various customer response models, in which the response variable is the probability of whether a customer with various characteristics will respond to a direct marketing campaign. Unlike those response models, the objective of this paper is to analyze the customers’ response patterns and speed over time.
For observational data on the number of responses over time, an S-shaped sigmoid function can be used to describe and predict the growth pattern of customer responses (Freeland and Weinberg 1980). For example, McGowan (1986) proposed a logistics curve with five unknown parameters, which have no meaningful interpretations. In this paper, we proposed a probabilistic model with three parameters that can be interpreted as the ultimate response rate, daily delay rate, and total delivery time. Furthermore, we showed that the geometric response model with a Poisson delivery time has many desirable properties.
Our response model was fitted to Huxley’s (1980) empirical data to show its superior performance over conventional models. However, Huxley’s response data has the following anomalies: The first week is only two days, while other weeks each have five days. In addition, follow-up mails were sent in weeks 4 and 7. To compare the performance of our proposed response model with that of conventional models, we may need more empirical data or extensive simulation studies. In any case, we believe that our response model with the Poisson delivery is clearly an improvement over the traditional growth curve models.
Certainly, it is possible to construct richer and more complex response models with more model parameters. For example, we assume that the delay rate q is constant throughout the entire process, but it could be a function of time or could be changed by some form of follow-up or reminder mailings. Although we only considered a discrete-time case in this paper, our response model could be extended to a continuous-time case, in which each time period is not necessarily the same. This can be achieved by making appropriate modifications to our geometric response model with varying degrees of difficulty.
Another potentially fruitful area of research lies in a Bayesian response model that could incorporate our prior knowledge from similar direct marketing campaigns or expert opinions (Rossi and Allenby 2003). Unlike other conventional response models that only give point estimates of unknown parameters, the Bayesian model can construct confidence intervals of parameters and test various hypotheses under different loss functions. The geometric response model in this paper has three unknown parameters; however, the computational difficulties with the three prior distributions can be overcome with an appropriate Monte Carlo Markov chain method or a Gibbs sampler (Chun 2008).
With the increasing popularity of personal computers and the Internet, many researchers have analyzed the differences in shopping behavior of online customers (Van den Poel and Buckinx 2005). Thus, it would be interesting to compare the ultimate response rate, daily delay rate, and total delivery time between a traditional mail survey and a web-based survey (Cobanoglu, Warde, and Moreo 2001; Kwak and Radler 2002). We can also analyze the effects on the parameter values based on various response stimulants such as providing advance notice to respondents, utilizing different forms of postage, giving a variety of monetary and non-monetary premiums, and so on (Cobanoglu and Cobanoglu 2003).
Our response model can be applied to other areas as well. Meade and Islam (1998) reviewed various “diffusion models” for the spread of technological innovation or the penetration of a new product into the market. The response rate in a direct marketing campaign can be represented as a growth curve over time. Thus, it would be possible to use our geometric response model with a delivery time for diffusion models that describe the process of how new products get adopted over time (Tapiero 1983; Shore and Benson-Karhi 2007).