استفاده از فرمول رگرسیون لجستیک برای نظارت بر میزان استفاده ناهمگن برای خدمات مبتنی بر اشتراک

This paper explores the effect of heterogeneity across different classes of customers as well as their time dependent usage behavior on the purchase rate of multiple services supplied by a subscription-based service provider. It is shown that a suitable model for customer usage pattern based on the logistic regression can effectively be employed to represent both the cross correlation and serially correlation of purchase rate for different kinds of services. Then the deviance statistic is proposed as an appropriate control statistic to simultaneously monitor the usage of multiple services. On the basis of three comparative scenarios, simulation results indicate that the power of the deviance-based control chart is considerably greater than some traditional counterparts like Hotteling’s T2 control chart. Research findings provide promising results for marketing managers and practitioners in terms of both better understanding of the behavior of different classes of customers as well as timely evaluation of investment opportunities that can lead to enhancement of the firm’s relationship with customers.

This paper deals with employing an appropriate statistical method for monitoring usage pattern of various services supplied to multiple classes of customers by a subscription-based service provider. This type of enterprise may involve a broad spectrum of service industries such as telecommunications, insurance services, internet service providers, as well as many internet-based service firms like online content providers. Such corporations can operate on either contractual (i.e., subscription-based model) or non-contractual basis (i.e., pay per use) (Dover & Murthi, 2006). This paper investigates the contractual business model or the so-called subscription-based services. Customers of such a firm usually purchase a quarterly, an annual, or an “annual billed monthly” subscription. Momentarily changes of customer needs along with the rapid alterations of market conditions demand to have a prompt reaction against unusual shifts in customer usage pattern. Such flexibility can be gained through a responsive monitoring mechanism, which can detect significant changes in customer behavior via exploration of usage data. Statistical process control (SPC), extensively used to monitor quality characteristics in manufacturing processes, consists of problem-solving tools suitable for monitoring purposes in service industries. Nonetheless, little research has been done on the application of SPC methods to the monitoring of customer activities so that appropriate marketing campaigns and service customizations can be developed (Jiang, Au, & Tsui, 2007). An overview of literature, especially studies that investigate the application of SPC charts for service usage monitoring, is provided in the rest of Section 1. To reduce customer churn, Pettersson employs multivariate T2 control chart to develop an early warning system, which monitors the proportion of likely churned customers in telecommunication industry ( Pettersson, 2004). Qian, Jiang, and Tsui (2006) employ functional mixture models to derive the profile of customer transactions in a given period of time. Based on the estimated profile, a monitoring method, which resembles the profile monitoring in SPC has been proposed to predict customer churn. Recently, a SPC framework has been introduced for business activity monitoring which can be applied for the purpose of prevention of customer churn and detection of fraud in financial transactions ( Jiang et al., 2007). Multi-way principle component analysis (MPCA), a statistical process monitoring technique in batch production systems, has been also used for fraud detection in the service sector ( Tsung, Zhou, & Jiang, 2007). Using probability models to model customer time dependent non-homogenous usage behavior, makes it possible to employ inferential statistics in order to develop a parametric monitoring model. Mixture probability models (Fader and Hardie, 2007 and Johnson et al., 2004) and Markov chain models (Chen and Cooper, 2002, Ha et al., 2002 and Pfeifer and Carraway, 2000) are prominent methods that have been successfully used to capture heterogeneity of customer behavior as well as its time dependency. Logistic regression model is employed in this research to construct a predictive model of the probability of usage for multiple services proposed by a service provider. This approach provides the possibility to represent heterogeneity across customers regarding their intention toward various services. It is shown that the cross correlation across multiple services can be represented using this approach, though it is assumed that purchases from different types of services are performed independently. Logistic regression has also been widely used and investigated in predictive data mining to predict customer churn in retail industry (Buckinx & Van den Poel, 2005), financial services (Larivie & Van den Poel, 2005), telecommunications (Ahn, Han, & Lee, 2006), as well as subscription-based services (Burez and Van den Poel, 2007 and Coussement and Van den Poel, 2008). The idea of employing SPC charts using logistic regression model to monitor usage behavior originates from the rich literature on model-based control charts commonly used in multistage production processes (Loredo, Jearkpaporn, & Borror, 2002). Recently, generalized linear regression models including Poisson and logistic regression models have been employed to derive suitable monitoring methods in situation where key output characteristics of process or product quality are multivariate discrete random variables and are affected by upstream process stages. Jearkpaporn et al., 2007, Skinner et al., 2003 and Skinner et al., 2004 are recommended to be referred in this respect. Integrating SPC charts with predictive models of customer usage in order to facilitate monitoring customer behavior is the main objective of our research. The remainder of this paper is organized as follows. Next section provides precise definition of the problem. Section 3 deals with how to use logistic regression to model heterogeneous usage behavior across multiple classes of customers. Monitoring statistics are also derived in this section. To compare the performance of the proposed method with that of the other competing approaches, three illustrative cases are studied in Section 4. Section 5 outlines final remarks and conclusions.

Quick detection of any significant changes in customer usage behavior is of great importance for providers of subscription-based services. Such changes often reveal creeping trends in customer attitude toward using proposed services and could provide useful information for retention programs if recognized at the right time. Service industries such as telecommunications or online content providers propose various services to their customers for a given time interval. Produced by a series of indicator variables each of which denotes a particular service, a binary vector can represent the usage pattern of each customer at a given time period. Time dependent non-homogeneous behavior of customers causes the purchase rate of various services to form an auto-correlated multivariate Bernoulli distribution whose monitoring over time requires employing rather complicated statistical methods. Assuming a well-segmented market, this paper proposes a suitable probability model of customer behavior that can justify the inter-correlations among services and also the autocorrelation between successive values of service usage over time. In this paper, logistic regression models have been employed to represent heterogeneity across different classes of customers. To account for time dependent usage behavior, it is assumed that transition of customers across different classes takes place according to a Markov chain model. Having been recommended for evaluating the goodness of fit in generalized linear models, the concept of deviance statistics is employed here to produce control statistics for monitoring usage rate of a number of services. As the result of simulation procedures for three illustrative cases, this study concludes that control charts using deviance statistics can considerably improve the detect ability against changes of model parameters in comparison with more conventional methods such as Hotteling’s T2 control chart. Recognizing customer segments that have experienced a behavioral change is the next important stage after detecting unusual variation of customer usage rate. In this study, useful information provided through decomposition of the deviance statistic is utilized to diagnose the out of control situation. Thus, the proposed procedure can be effectively employed to provide useful information about how to differentiate between usual and unusual customer usage behavior as well as how to recognize particular group of customers whose tendency toward service usage has changed (either in a decreasing or an increasing direction) over time. Although the primary goal of this research was to assess the capability of a model-based control method called deviance statistic in monitoring purchasing behavior of customers for subscription-based services, a more exact study revealed that Pearson’s chi-square statistic performs as equally as and sometimes better than the deviance-based control charts. Although both deviance and Pearson statistics have the same asymptotic distribution, uncertainty about properties of Pearson statistic in small samples (Hogg & Tanis, 1983) persuades us to defer a conclusive comment about their performance in comparison with each other until a more through comparative study is executed. To extend and improve this study, a suitable area can be to use more sensitive methods in order to shorten the delay between change point and detection time. Using monitoring methods, which accumulate information over time like cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts, has proved to be especially helpful in detecting small persistent changes in process distribution parameters. As emphasized in an interesting comment by paper reviewers, using control charts that besides considering usage heterogeneity are able to employ the information accrued over time can be promising in terms of increasing the sensitivity of monitoring procedure with respect to small shifts of customers’ usage rate. Concerning this issue, there have been several remarkable papers in healthcare surveillance, which have employed a similar approach for monitoring clinical treatment and hospital care quality indicators considering heterogeneity across patients (Biswas and Kalbfleisch, 2008, Sego et al., 2009 and Steiner and Jones, 2010). For example, Sego et al. (2009) investigate the use of logistic regression to design a CUSUM chart for monitoring the post-operative mortality after a surgical operation. They also propose a more effective tool, which uses a time-to-event regression method instead of a binary-response regression method. Steiner and Jones (2010) propose an EWMA procedure for monitoring patients’ survival times after cardiac surgery using a particular risk score for each patient. Biswas and Kalbfleisch (2008) also use risk-adjusted CUSUM control chart to assess the quality of kidney transplant operations. They have used Cox proportional hazard regression model to take heterogeneity across subjects into account. Altogether, the recent advances in model-based monitoring procedures lead us to think about the integration of a memory-based chart with a successful diagnosing mechanism as an area that deserves further investigation. The result may provide both quick detection as well as the possibility of taking appropriate corrective actions. Lastly, in this paper we just considered situations where a firm records customer usage from various services by a binary vector. Therefore, an interesting area to expand the applicability of the model could be to use heterogeneity models, which can address the quantity of usage as well. Truncated regression models like Tobit model have been especially recommended by paper reviewers for this purpose.