مقایسه جایگزین ها برای عدم همبستگی نامتعارف در مدل های بازاریابی مستقیم  Comparing alternatives to account for unobserved heterogeneity in direct marketing models

1. Introduction Marketers are always interested in assessing how customers respond to marketing actions. In the area of direct marketing these actions often constitute of mailings that are sent to customers. Advertising spendings in the catalog mail order industry amount to around 8 billion U.S. dollars, which is about four times higher compared to spendings in 2010, which means that direct mailings are still an important marketing instrument despite the increase of online channels (statista, 2016). Response models can capture customer reactions and help target future mailings to these customers to induce further purchases. For a comparison of various data mining techniques see Olson and Chae (2012). However, as customers differ from one another, e.g., some customers react differently to the same marketing actions, it is important that marketers take heterogeneity of customers into account (Guelman, Guillen, P ´ erez-Mar ´ ´ın, 2015 ). Neglecting heterogeneity may lead to biased parameter estimates (Popkowski Leszczyc & Bass, 1998). On the other hand, a survey of Verhoef, Spring, Hoekstra, and Leeflang (2002) shows that only 27% of companies employ segment specific models. Generally, different responses to mailings can be due to observed and unobserved heterogeneity. Observed heterogeneity can be assessed by customer specific variables. Unobserved heterogeneity is usually modeled with either a continuous or discrete mixture of distributions of parameters. Discrete mixtures of distributions are addressed with either a finite mixture (e.g., Gon¨ul, Kim, & Shi, 2000) or a Mixture of Dirichlet ¨ Processes (MDP) (e.g., Ansari & Mela, 2003). A continuous mixture is usually addressed with mixtures of normal distributions (e.g., van Diepen, Donkers, & Franses, 2009). Both a finite mixture and a MDP divide customers into several segments and treat customers of the same segment equally. These two approaches are in contrast to a continuous mixture able to reproduce multimodal and skewed distributions (e.g., Hruschka, 2010). The MDP provides the number of segments as one of the estimated parameters. This property can be seen as an advantage as researchers using a MDP do not need to estimate several finite mixture models each with a different number of segments. Our study contributes to the literature on direct marketing models in the following way. We compare three specifications of unobserved heterogeneity and investigate which of these specifications performs best in terms of model fit. To the best of our knowledge, no previous study dealing with effects of mailings has done that before. In addition, we compare how estimation results are affected by the specification of unobserved heterogeneity. We finally address different managerial implications that may result due to different specifications. The remainder of the article is structured as follows. The following section addresses findings of selected direct marketing related studies on unobserved heterogeneity. Model specifications and our estimation method are discussed in the third section. Section 4 informs about the data set. Section 5 contains estimation results and managerial implications. In the last section we conclude the article.