Click for Customer Conversion
An analysis of event-based travel data to predict purchase probabilities through
online touchpoint contacts
Click for Customer Conversion
An analysis of event-based travel data to predict purchase probabilities through
online touchpoint contacts
Daniël Silvian Lutjens University of Groningen Faculty of Economics and Business
MSc Marketing Intelligence Master Thesis
18-06- 2018
Daniël Silvian Lutjens Haddingestraat 41b 9711KC, Groningen (+31) 6 36 15 28 63 daniellutjens@gmail.com S2523582 Supervisor (First): dr. P.S. (Peter) van Eck
p.s.van.eck@rug.nl Supervisor (Second): prof. dr. T.H.A. (Tammo) Bijmolt
t.h.a.bijmolt@rug.nl University of Groningen Faculty of Economics and Business
Management Summary
Traditionally, the customer buying journey is a very one-sided process: The customer indicates interest, gathers information, purchases and looks for post-sale support. The introduction of the Internet has facilitated the emergence of a new marketing era where customers and companies get into contact several times via multiple platforms. Each contact has its own influence on the progress of the customer journey. As a consequence, the online customer journey is evermore interactive and diverse. Although previous research has studied a wide array of topics related to the online customer journey, it has also left significant
knowledge-gaps. This study offers a new angle in customer journey literature by analyzing and predicting individual purchase probabilities from a time-based perspective. Additionally, it considers the number of touchpoint contacts as a predictor for conversion. Being able to successfully predict which customers are likely to convert can aid in the targeting of marketing tools, as well as in the optimization of advanced marketing algorithms such as real-time bidding (RTB). Hence, this study seeks to answer the following research questions:
1. How does touchpoint intercontact time in the customer purchase journey influence the propensity to purchase?
2. How does customer purchase journey length, measured as number of touchpoint contacts, influence the propensity to purchase?
Based on a comprehensive analysis of available literature, three hypotheses are developed. The first of which expects intercontact time to follow an inverted U-shaped relationship with purchase probabilities. The second hypothesis theorizes that an increased number of
touchpoint contacts positively influences purchase probabilities. Finally, a moderating effect is hypothesized: A larger share of customer-initiated contacts (CICs), rather than firm-initiated contacts (FICs), in a customer journey is anticipated to enhance the effect of the number of touchpoint contacts on purchase probability.
The findings of this research are as follows: Partial support for the inverted U-shaped relationship between intercontact time and individual purchase probabilities is established. The existence of an ideal-point relationship becomes apparent from the GAM analyses, but it turns out to be more complex than hypothesized. The inclusion of dummy variables in the GLM leads to the insight that purchase probabilities peak at an average intercontact time of about 10.000 seconds (~ 3 hours), after which purchase probabilities gradually decline. This could indicate that two groups of customers are represented in this study: One group that looks for holidays with the intention to purchase and another with no intention to buy, but rather with a recreational browsing motive. As such, intercontact time can be of classifying and predictive value. Furthermore, the research provides compelling evidence that an increased number of touchpoint contacts positively influences the tendency to purchase. For each additional contact, the probability to convert increases with 0,00019. For managers, this provides incentive to stimulate additional contacts both directly (e.g. through retargeting) and indirectly (e.g. through improved website design). Finally, no moderating effect of the share of CICs in a customer purchase journey can be established, although an analysis of the effect of the number of touchpoint contacts on separate CIC and FIC datasets reveals a larger effect under the FIC condition.
Future research should aim at determining a definite answer regarding the effectiveness of CICs and FICs, as well as the exact role of intercontact time in shaping purchase
probabilities. Also, replicating the study on different samples is required to ensure
Preface
When I arrived at the University of Groningen in 2013 for my bachelor in International Business, I did not have the slightest clue which aspects of business research would appeal to me most. Yet, I am certain that I would have never guessed that my interests would lie in the field of data analysis and statistics. Throughout my time at the Faculty of Economics and Business, I have had the privilege to discover the academics behind business together with countless of inspiring students, professors and eventually even colleagues. Together with them, I discovered my enthusiasm for data-analysis. During my board year at the Marketing Association of the University of Groningen (MARUG), it became clear to me that the master program for Marketing Intelligence could offer me an academic specialization in the field of marketing, with a data-driven and statistical angle.
Over the course of the last year, I have been participating in this program and it has brought me lots of enjoyment and knowledge. For this, I want to thank the passionate, supportive and professional team of (assistant-)professors and faculty staff. If you are reading this, you are looking at my concluding research project: the master thesis that I have been working on for the semester. During the both extensive and intensive process of writing my thesis, I have been assisted by my first supervisor dr. Peter van Eck. I want to express my gratitude towards him for the time he has taken reading my preliminary work and providing timely and
constructive feedback, whilst always stimulating me to stay proactive and to look for answers rather than asking for them. Besides that, I want to extend my gratitude towards prof. dr. Tammo Bijmolt, who has taken the time and effort to act as my second supervisor. Finally, I also want to thank the fellow-students in my thesis group for always being supportive and reassuring.
Table of Contents
1. Introduction ... 1
2. Theoretical Framework ... 3
2.1. The Online Customer Journey ... 3
2.2. Time and the Online Customer Journey ... 6
2.3. Customer-initiated Contact vs. Firm-initiated Contact ... 7
3. Research Design ... 9 3.1. Data Collection ... 9 3.2. Variables ... 10 3.3. Choice of Technique ... 11 3.4. Curvilinearity ... 12 3.5. Moderation ... 12 3.6. Model Specification ... 12 3.7. Plan of Analysis ... 13 4. Results... 15 4.1. Preliminary Checks ... 15 4.2. Descriptive Statistics ... 17
4.3. Assumptions for Logistic Regression ... 18
4.4. Model Selection ... 19
4.5. Hypothesis Testing ... 22
4.6. Model Re-estimations... 24
4.7. Generalized Additive Model ... 28
5. Discussion and Outlook ... 33
5.1. Intercontact Time ... 33
5.2. Number of Contacts ... 35
5.3. Share of CICs ... 36
5.4. Implications ... 37
5.5. Limitations and Future Research ... 38
6. References ... 40
7. Appendices... 48
7.1. Appendix A: Descriptive Statistics ... 48
7.2. Appendix B: Binary Logistic Regression Estimation Results ... 50
7.3. Appendix C: Binary Logistic Regression Curves ... 55
7.4. Appendix D: Binary Logistic Regression Re-estimation Results ... 56
1. Introduction
According to a report by Borrell Associates Inc. (2016), about 12.2 percent of all digital marketing services spending in the US exists of “online marketing support”. Of these expenses, about 87.5 percent exists of spending related to Search Engine Optimization (SEO). It is forecasted that SEO-spending will rise to over $80 billion by 2020.
This report is only one example of a long list of indicators that forecast massive growth for online marketing-related spending. Similar forecasts can be found in academic literature (e.g. Ho and Dempsey 2010), conference proceedings (e.g. Kirtiş and Karahan 2011) and several online sources (e.g. American Marketing Association 2017; Marketing Dive 2018).
The evolution of online marketing has led to changes in the marketing landscape, mainly by altering the concept of the ‘customer journey’. Traditionally, the customer (buying) journey can be described as “starting from the moment customers initially indicate interest, through the time they spend gathering information, to when they complete a transaction and seek post-sale support” (Peterson et al. 2010). Since the introduction of the Internet, the number of online media channels has increased rapidly. As a result, the offline customer journey
adapted to the online environment and new interpretations of the customer journey arose. An example of this is the new network structure commonly referred to as the “path to purchase” (P2P) (Achrol and Kotler 2012; Srinivasan, Rutz, and Pauwels 2016). This new, online customer journey exists on the one hand of advertisers employing a plethora of marketing channels (e.g., SEO, social media and e-mail) to reach their potential customers and on the other hand of customers engaging in information search through search engines (e.g. Google) and company websites unilaterally (Anderl et al. 2016). Consequently, customers may come into contact multiple times with different channels before actual conversion takes place. Each of these contacts has an influence on the subsequent steps in the path to purchase through carryover effects (i.e. lag between the exposure to a touchpoint and a customer’s reaction), exposure to additional information and spillover effects (i.e. cross-channel effects) (Li and Kannan 2014).
researchers is “customer journey mapping”, where graphical tools are employed to create a visual overview of the customer journey (e.g. Anderl et al. 2016; Rosenbaum, Otalora, and Ramírez 2017; Wolny and Charoensuksai 2014).
Although these studies shed light on several aspects of the online path to purchase,
unexplored terrain still exists. Surprisingly little research has focused on the role of time in the process. Anderl et al. (2016) explicitly called for research into “the timing between
contacts along the customer journey”. The academic contribution of this research is to answer this call and look for ways in which touchpoint contact and time variables can contribute to understanding a customer’s propensity to purchase. The application of a new, time-based perspective fills an existing academic gap and by responding to the suggestion of Anderl et al. (2016), it adds to the current customer journey literature. In addition, it will provide new insights on the influence of the online customer journey length (measured as the number of touchpoint contacts) in predicting individual purchase probabilities. Some studies have already incorporated customer journey length (e.g. Anderl et al. 2016), or even relationship length (e.g. Wang and Wu 2012), in their models. However, no study to date has put an exclusive focus on the number of touchpoints in the customer journey as a predictor of individual purchase probabilities.
This research also has significant practical relevance: Being able to classify or predict the chances of conversion for individuals in the online customer journey is extremely important, since for most businesses 80% of their revenues can come from just 20% of their customers (Cook and Mindak 1984). If firms are able to identify (preferably in real time) the individuals that are most likely to convert, marketing tools can be successfully employed to stimulate this. The online customer journey allows for a shift from aggregate mass-marketing - where no distinction is made between high and low quality prospects - to a more focused direct marketing approach (Kaefer, Heilman, and Ramenofsky 2005). Kumar, Venkatesan, and Reinartz (2008) found that customer-focused sales campaigns are much more effective when sales attempts are made only at moments in time at which customer are expected to purchase. Moreover, information about purchase likelihood was linked to both higher effectiveness and efficiency.
information that becomes available (Wang, Zhang, and Yuan 2016). Consequently, further exploration of this topic would allow for future academic research not only in the field of marketing, but also in areas such as data science, computer science and artificial intelligence. Considering the theoretical and practical relevance of research into the prediction of
individual purchase probabilities by means of customer journey touchpoints, this research will focus on this highly relevant and remarkably unexplored topic. Two areas of interest will be included in this study: One is the role of intercontact time and the other is customer
journey length, measured as the number of touchpoints in the customer journey. These themes will be assessed by analyzing event-based, online data from a Dutch travel agency that wishes to remain anonymous. By doing so, this research will seek to answer the following questions:
1. How does touchpoint intercontact time in the customer purchase journey influence the propensity to purchase?
2. How does customer purchase journey length, measured as number of touchpoint contacts, influence the propensity to purchase?
To answer the questions above, this report will proceed in the following way: In the
upcoming section, academic literature will be employed to elaborate on the topics at hand and form the hypotheses. Afterwards, the research design will be discussed, including information on the data, research methods and analyses. Then, the results of the data analyses will be presented and discussed, after which conclusions will be drawn and limitations and recommendations will be presented.
2. Theoretical Framework
2.1. The Online Customer Journey
the ‘customer journey’. In some research, these journeys are described as clearly delimited processes (Whittle and Foster 1989), whereas others argue that the customer journey is a more open-ended process with no set start or ending point (Nichita, Vulpoi, and Toader 2013). Also, the role of touchpoints in the process is subject to competing views: To groups of researchers, touchpoints form the basis of the journey (Meroni and Sangiorgi 2011; Stickdorn and Schneider 2011), while others rather focus on service encounters (Tax, McCutcheon, and Wilkinson 2013) or specific events (Crosier and Handford 2012).
As a result of the different understandings of the customer journey, combined with a general interest into the topic, an abundance of customer journey approaches were developed. These consist mainly of “methods and practices where the service process is analyzed, modeled, managed, or (re)designed applying a customer journey perspective” (Følstad and Kvale 2018). In marketing research, the customer journey takes several distinct, yet comparable, forms. Conventionally, the path to purchase goes through the following distinct stages: need recognition, pre-purchase search, evaluation of alternatives, the actual purchase, and post-purchase evaluation (van der Heijden, Verhagen, and Creemers 2003). In the pre-post-purchase stage, potential customers use both internal (e.g. long-term memory) and external (e.g. friends and/or marketing messages) information sources to form an idea of the
product/service to allow for the next step of the path to purchase: alternative evaluation (Pizam and Mansfeld 1999). Next to the one described above, other frameworks have been developed: Court et al. (2009) developed a model including awareness, familiarity,
consideration, purchase, and loyalty, and Lemon and Verhoef (2016) boiled their model down to the prepurchase, purchase, and postpurchase stages. The common ground of these separate frameworks is their focus on the complete customer decision process, from awareness to (post-)purchase (Lee 2010).
First of all, the introduction of the Internet provides significant benefits for both customers and managers. For the former, the main perquisite is that the search for information gets much easier. Usually, information-seeking requires a trade-off between the additional search costs and the benefits of obtaining more information on the alternatives (Hauser and
Wernerfelt 1990). The Internet decreases the cost of searching and enhances the decision quality (Häubl and Trifts 2000). From a business perspective, managers are benefited by the availability of more data. Nowadays, customer behavior analyses are often performed by combining one of the customer journey approaches mentioned in the previous paragraph with web analytics (Anderl et al. 2016; Lee 2010; Muret 2013) or customer relationship
management (CRM) systems (Buttle 2009). Online customer journeys generate clickstream data that record a website user’s navigational path and allow for path specific analyses (Montgomery 2001). Such data enable the development of insights on individual customer’s goals, knowledge and interest, as well as sequence data (Montgomery et al. 2004). Online customer data has been utilized often to predict purchase conversion from aggregate, session-level web browsing behavior data (Moe et al. 2002; Moe and Fader 2004; Park and Fader 2004). Since the actual sequence of the clickstream can contain lots of important information, others have engaged in sequence-based analyses (Montgomery et al. 2004; Sismeiro and Bucklin 2004).
On the other hand, the Internet also creates difficulties. According to van der Heijden, Verhagen, and Creemers (2003), two major variations exist between online and offline shoppers. First of all, customers that purchase goods and services online have no choice but to interact with technology during their purchase journey. Since the physical purchase environment is replaced by an electronic equivalent, technical issues related to information systems and human computer interaction are expected to arise. One can think mainly of usability issues like effectiveness and efficiency of such systems (O’Keefe et al. 2000). Secondly, shoppers require more trust in an online shopping environment than in a physical one. Trust has been known to be an important aspect in online shopping, since it can alleviate insecurities and uncertainty related to unknown shops, owners, product quality and
2.2. Time and the Online Customer Journey
Along their purchase journey, customers get in contact with several touchpoints via a multitude of channels and devices. With more marketing channels comes a larger variety of touchpoints, meaning that customers can get into contact with, for example, advertisements, search queries, e-mails and peer-to-peer encounters like word-of mouth (Baxendale,
Macdonald, and Wilson 2015; Kannan, Reinartz, and Verhoef 2016). Venkatesan and Kumar (2004) performed a study on how customer lifetime value (CLV) could be increased through customer relations. One of the variables in their analysis was ‘intercontact time’, which they operationalized as the “average time between two customer contacts by the supplier across all channels of communication between two observed purchases” (Venkatesan and Kumar 2004, p. 111). In this research, ‘intercontact time’ will also be used as a variable under the
following operational definition: ‘the average time between two touchpoint contacts across all channels of communication in the customer purchase journey’.
As stated before, online purchases require a high level of trust. According to Morgan and Hunt (1994), increased marketing communications help to establish trust between a buyer and seller and as such create commitment. In their research, they state that “relevant, timely, and reliable” communications will lead to greater trust. This suggests that a more ‘intense’ (i.e. shorter intercontact time) path to purchase will lead to more trust and therefore higher propensity to purchase. On the other hand, Fournier, Dobscha, and Mick (1998) argue that dysfunction in a relationship can occur when too much communication takes place. Moreover, the additional information a customer receives from an extra contact in a short period diminishes fast (Venkatesan and Kumar 2004). In light of these studies, too short intercontact times can be considered intrusive and inefficient. Accordingly, it is reasonable to expect a non-linear relationship, where an optimal point in intercontact time exists. Thus:
H1: An inverted U-shaped relationship exists between the average touchpoint intercontact time and a customer’s predicted purchase probability.
Furthermore, Manchanda et al. (2006) find that “the number of exposures, number of Web sites, and number of pages on which a customer is exposed to advertising all have a
increases positive affect (Bornstein 1989; Maslow 1937; Zajonc and Markus 1982). In general, a larger number of exposures leads to enhanced familiarity, which in turn positively affects liking (Zajonc and Markus 1982).
Familiarity does not just increase liking through mere-exposure. In a wide range of settings, familiarity is also found to breed trust (Gulati 1995; Lubell 2015). As stated before, shoppers require more trust in an online shopping environment than in a physical one. Trust is an important tool to mitigate perceived risk, which is especially present in e-commerce settings (Kim, Ferrin, and Rao 2008; Luhmann 2000). Consequently, it is reasonable to expect a longer customer journey to positively affect trust and thus purchase probabilities.
In addition, a larger number of touchpoints in a customer’s path to purchase could indicate more serious buying behavior, or an increased intention to actually purchase a product. It makes sense to assume that customers are willing to spend more (customer journey) time on products for which they have an intention of buying. Ajzen (1985) developed the ‘theory of planned behavior’, which predicts behavior through intention. In other words, the more a person intends to purchase a product, the more likely it becomes that he/she actually does buy. Hansen, Jensen, and Solgaard (2004) found that the theory can also be applied to online shopping situations. In line with this, it can be expected that increased purchase intention in the online customer journey also increases purchase probability. Assuming that a longer customer journey indicates higher purchase intention, combined with the arguments above, it is hypothesized that:
H2: A positive relationship exists between the number of touchpoints in the path to purchase and a customer’s predicted purchase probability.
2.3. Customer-initiated Contact vs. Firm-initiated Contact
Contact between firms and customers can have two distinct forms. Instances where firms actively ‘push’ their message to their customers through, for example, advertising are known as firm-initiated contacts (FICs). Customers might also ‘pull’ desired information to
2008).
Academic research describes that, in general, CICs are significantly more effective than FICs. This is mainly due to the fact that they stem from customers’ own interests and are therefore perceived as less intrusive than FICs (e.g. Sarner and Herschel 2008; Shankar and Malthouse 2007). De Haan, Wiesel, and Pauwels (2016) find significant elasticities for FICs in 53.3% of the studied cases, while CICs obtain significant elasticities 70% of the time. Their results quantitatively prove the outperformance of CICs compared to their firm-initiated
counterparts.
A possible explanation for the difference in effectiveness can be found in the sequence of the customer journey. As has already been discussed, this is made up of several steps ranging from need recognition to the (post-) purchase stage. Generally, FICs are found in the early stages of the path to purchase or even before that: When targeting (potential) customers that have not yet recognized a specific need. CICs, however, are often found in the later stages of the journey, such as alternative evaluation or purchasing, where purchase intentions are generally already higher (de Haan, Wiesel, and Pauwels 2016).
Altogether, CICs are proven more effective than FICs, are considered as less intrusive by customers and occur generally in later-funnel stages where purchase intentions are overall higher. Hence, it is to be expected that each additional CIC is more influential in determining purchase probability than each additional FIC. In other words, one can expect fewer CIC than FIC touches to be required for increased purchase probability. Thus:
H3: As the share of customer-initiated contact in a customer journey increases, the relationship between the number of touchpoints in the path to purchase and a customer’s predicted purchase probability strengthens.
Fig. 1. Conceptual model of present research.
3. Research Design
3.1. Data Collection
In order to test the hypotheses and answer the research question, event-based, online data from a Dutch travel agency will be analyzed. The data were provided by GfK, a German market research institute, and collected through the GfK Crossmedia Link. This panel passively measures and collects the complete information chain, including exposure and media consumption, orientations and purchases. Passive measurement entails constant measurement of consumer behavior through for example browser plug-ins or audio devices. For this research, data were obtained from the Dutch travel agency for a period of one year and four months, from June 1st 2015 until September 30th 2016. The data can be classified as panel (or longitudinal) data, which means that time-series data are recorded for each member in the dataset (Leeflang et al. 2015). Moreover, the data are event-based, meaning that each observation corresponds with a specific event. In this case, an event means a touchpoint, either customer- or firm-initiated.
The dataset used in this research contains information on 24.002 orientations (i.e. customer purchase journeys) of 7.312 users. It is the result of the merger of two individual datasets with different kinds of information. The first one records a grand total of 2.456.528 events for 7.312 users, existing of 29.012 orientations, 3.674 purchases and 192 focal brand purchases. The second dataset contains information on the demographic characteristics of 9.678 users on 21 variables. These demographics correspond with individual users from the first dataset. Certain demographic variables will be used in the model specification and estimation as control variables.
3.2. Variables
The aim of this research is to establish a model that uses customer journey timing and touchpoint variables to predict the conversion probabilities of individual customers. To realize this, a model will be developed including the following variables from the GfK dataset: PurchaseID (i.e. a unique ID to identify individual purchase journeys) and purchase any (i.e. indicator whether a booking was made at any travel agency in a particular purchase journey). In addition, the following variables will be calculated from the data: Intercontact time (i.e. average time between any two touchpoint contacts in any purchase journey), number of touchpoint contacts (i.e. total number of touchpoint contacts in any purchase journey) and share of CICs (i.e. number of CICs relative to the total number of touchpoints in any purchase journey).
The operationalization of intercontact time is based on the following definition from
Venkatesan and Kumar: “average time between two customer contacts by the supplier across all channels of communication between two observed purchases” (2004, p. 111). In this research, two alterations to this definition will be made. First of all, instead of merely
including the customer contacts by the supplier, all touchpoint contacts will be considered, as each touchpoint in the journey adds a separate influence to the purchase probability (Anderl et al. 2016; Li and Kannan 2014). Therefore, when this report speaks of ‘intercontact time’, the time between any two customer journey touchpoints is meant, whether instigated by the firm or the customer. Secondly, in this research the focus will be on the complete customer journey, rather than just the contacts “between two observed purchases” (Venkatesan and Kumar 2004). In short, ‘intercontact time’ is in this research defined as ‘the average time between two touchpoint contacts across all channels of communication in the customer purchase journey’.
Table 1. Academic grounds for control variables.
Demographic Variable Literature
Region
Size of municipality
“Internet use and online buying are still largely urban phenomena in the Netherlands” (Farag et al. 2006).
Gender
Gender differences exist in e-commerce settings, e.g.: ● Men shop and purchase more online than women
do (Rodgers and Harris 2003);
● Men and women have different intention when shopping online (e.g. Rodgers and Harris 2003; Sánchez-Franco 2006);
● Females value online shopping less than men (Hasan 2010).
Income Education Age
“The higher a person’s income, education, and age, the more likely that person will buy online” (Bellman, Lohse, and Johnson 1999).
3.3. Choice of Technique
This research is both causal and quantitative. The dependent variable in this research is binary: A customer either purchases a product or does not. According to Leeflang et al. (2015), marketing problems with a binomial response variable require a binomial logit/probit model. In such models, there are two discrete possible outcomes: 0 and 1. Therefore, a key characteristic of such a model – i.e. the sum of the probabilities of observing the discrete outcomes equals 1 - is formulated below:
3.4. Curvilinearity
Since an inverted U-shaped relationship is expected in H1, the model has to accommodate this. In order to introduce curvilinearity into a linear regression model, polynomial terms (e.g. quadratic or cubic terms) can be included. The same holds for logistic regression models (Osborne 2014). To test for presence of (inverted) U-shaped relationships in logit models, it is common practice to include both the original independent variable and its squared term in the model (e.g. Haans, Pieters, and He 2016; Lind and Mehlum 2010). Therefore, the model will include both intercontact time and intercontact time (squared).
3.5. Moderation
The concept of moderation entails that “the predictive efficacy of an independent variable and/or the form of the relationship may vary systematically as a function of some other variable(s)” (Sharma, Durand, and Gur-Arie 1981, p. 291). In other words, the size/effect of a given relationship depends on the value of another variable. A synonym for moderation is ‘interaction’. Although this definition stems from ANOVA statistics research rather than regression, the terms are nowadays used interchangeably (Baron and Kenny 1986; Marsh et al. 2013). To add moderation to a model, model builders include a product term of the two variables that are expected to interact (Leeflang et al. 2015). To test the moderation effect as hypothesized in H3, an interaction term between number of contacts and share of CICs will be included. For this to be possible, the model also has to include the main effect of share of CICs.
3.6. Model Specification
According to Rodriguez (2007) the specification of a binary logit model originates from a linear probability model as provided in the equation below:
𝜋" = 𝑥′𝛽
However, this specification method has no guarantee that the predictor variable values will be within the desired (zero to one) range. Therefore, the equation is log-transformed and will look as follows:
𝜂" = logit (𝜋") = log 𝜋" 1 − 𝜋"
𝜋" = exp {𝑥"6𝛽} 1 + exp {𝑥"6𝛽}
Which, according to Allison (2012, p.18), can be reformulated as: 𝜋" = 1
1 + exp (−{𝑥"6𝛽})
Following this notation, the model specification for this research is as follows: 𝜋" = 1
1 + exp 9− 9𝛽:+ 𝛽;𝐼𝑇" + 𝛽>𝐼𝑇"> + 𝛽?𝑁𝐶" + 𝛽B𝐶𝐼𝐶" + 𝛽C(𝑁𝐶 ∗ 𝐶𝐼𝐶)" +
𝛽E𝑅" + 𝛽G𝑆𝑀" + 𝛽J𝐺" + 𝛽L𝐼𝑁𝐶"+ 𝛽;:𝐸𝐷𝑈" + 𝛽;;𝐴𝐺𝐸" QQ Where:
𝜋" = Probability that a customer converts in purchase journey 𝑖; 𝐼𝑇" = Average intercontact time in purchase journey 𝑖;
𝐼𝑇"> = Average intercontact time squared in purchase journey 𝑖;
𝑁𝐶" = Number of touchpoint contacts in purchase journey 𝑖; 𝐶𝐼𝐶" = Share of CICs in purchase journey 𝑖;
(𝑁𝐶 ∗ 𝐶𝐼𝐶)" = Interaction term of number of touchpoint contacts and share of CICs in purchase journey 𝑖;
𝑅" = Factor variable for region of user in purchase journey 𝑖; 𝑆𝑀" = Size of municipality of user in purchase journey 𝑖; 𝐺" = Gender of user in purchase journey 𝑖;
𝐼𝑁𝐶" = Income of user in purchase journey 𝑖; 𝐸𝐷𝑈" = Education of user in purchase journey 𝑖; 𝐴𝐺𝐸" = Age of user in purchase journey 𝑖.
3.7. Plan of Analysis
In order analyze the data and estimate the model above, RStudio will be used. The first step in the data analysis process is data cleaning and preparation. The two separate datasets are merged and the variables that are required for the model estimation are calculated (if not provided in the dataset). Since the scope of the this research and its hypotheses is at the purchase journey level, the merged data will be aggregated by PurchaseID. Aggregation will always lead to some information loss, but the information that is required for this research will be maintained when using PurchaseID as the basis for aggregation. More specifically, for each aggregated PurchaseID, the sum of the number of touchpoint contacts, number of CICs and the number of FICs will be used. The latter are required to calculate the share of CICs. For intercontact time, an average will be calculated for each PurchaseID by dividing the sum of intercontact times by the number of touchpoint contacts in each purchase journey.
Data cleaning exists of “consistency checks” and “treatment of missing responses” (Malhotra 2009, p. 461). The former focuses on identifying and treating observations that are (logically) inconsistent and/or have extreme values (i.e. outliers), whereas the latter focuses on treating data points for which no value is provided. If outliers are found, these will be analyzed, discussed and treated. If missing values are found, their impact on the outcome of the analyses will be assessed. In case their impact is limited, no treatment is required. However, if they have substantial influence on the analyses, they will be treated with either Multiple Imputation or Expectation Maximization, two state of the art imputation methods. Also, the presence of collinearity between the variables in the data will be assessed. There is a
considerable chance of high multicollinearity between the intercontact time main effect and its quadratic term. In order to avoid this, the polynomials will be orthogonalized, reducing the possible multicollinearity problems with polynomials. If multicollinearity is detected for any other variable(s), the necessary steps will be performed to resolve the issue.
To get preliminary insights into the data, descriptive statistics and explanatory graphs will be provided once the dataset is prepared and scrubbed.
Next, the assumptions for logistic regression will be checked. Unlike the strict assumptions required for traditional Ordinary Least Squares (OLS) regression, logistic regression models have no strict assumptions for, for example, the residuals. Pituch and Stevens (2016) list four assumptions that are formally associated with logistic regression modeling. First, it is
assumed that the model used is correctly specified. Second, the cases are assumed to be independent. Third, each variable is assumed to have no error induced by their measurement and fourth, the sample size is sufficiently large enough.
The step thereafter is to estimate the model. According to Lani (2014), it is advisable to follow a stepwise approach when estimating the model. By doing this, one can easily assess the influence of the separate independent variables on the outcome variable. To estimate a binary logit model, Maximum Likelihood Estimation is applied (Malhotra 2009). In this research, the Generalized Linear Model (GLM) function will be used to run the estimations. The model fit of the different models will be compared to decide on which model to use for testing the hypotheses. The significance of the individual parameters in the chosen model will be assessed, as only the significant parameters can be interpreted and their influence
evaluated. The final step in analyzing the data exists of re-estimation of the model, if
4. Results
4.1. Preliminary Checks
A thorough look at the data revealed no oddities or inconsistencies. All observations fell within realistic and possible ranges. However, a look at the missing values indicated a substantial number of missing data for the demographics. All control variables missed data points for 2.762 of 24.002 observations, except for education level, where 3.753 observations were missing. For the variable income, a number of respondents indicated that they did not know the answer and/or did not want to answer the question. These observations were treated as missing values, increasing the number of missing values for ‘income’ to 6.119. Besides this, no missing values were found for any of the independent variables, nor for the
dependent variable. A large part of the missing values in the demographic variables could be explained by to the fact that there is a group of respondents in the panel that has not
participated consistently in every measurement. As a result, the demographics of this group were not matched to their purchase journeys by GfK. In order to confirm this, a t-test was conducted to compare the recorded journey length between the observations with and without missing values. If the missing values indeed relate to inconsistent participation, one would expect the recorded journeys to be shorter for the group with missing values. The test was significant with t(13.781) = 3,8704, p = 0,000 and confirmed that the group with missing values in the demographic variables has on average shorter recorded purchase journeys. This supports the expected relation between the missing values and the participation-rate of the respondents in the panel. As was suggested in the plan of analysis, the impact of the missing values on the model will be assessed to see if treatment is required. Since missing values only occur in the demographic control variables, these will be added to the model in stepwise fashion and comparisons will be made between models with varying numbers of control variables. By doing so, the influence of the missing values on the outcomes of the analysis can be established.
Next, an assessment of outliers was made for all variables by means of boxplots (for a boxplot overview, see appendix A.1). Almost all variables showed numerous values outside the boxplot-whisker range. However, for most variables these ‘outliers’ were considered non-problematic as they fall within a realistic range and are caused by the fact that for these variables, the majority part of the values is highly clustered or even identical (e.g. 22.128 of 24.002 entries for share of CICs are 1). Since a boxplot determines outliers based on
one observation was found to have an extreme value for the variable number of contacts. This specific observation indicated a total of 64.503 contacts while all other observations fell well below the 10.000 contacts. Since this contact was customer initiated, the same observation appeared as an outlier in the variable CIC. Due to extremely large deviation from the rest of the data, it is reasonable to classify this observation as wrongly recorded. Consequently, it was considered appropriate to remove this observation from the dataset. As can be seen in Figure 2 removing the outlier resolved the issue. The analyses were therefore performed with a total of 24.001 observations.
Fig. 2. Boxplot comparison (before and after outlier treatment).
Finally, a test for multicollinearity was performed. In order to check for multicollinearity problems in one or more of the independent variables, a linear multiple regression model was estimated. Then, the Variance Inflation Factor (VIF) scores were produced for the data. VIF scores are created by examining the extent to which each of the predictor variables can be expressed as a linear regression the others (Leeflang et al. 2015). VIF scores above 5 are worth additional investigation, whereas scores above 10 indicate high (and thus problematic) multicollinearity. Since the polynomial and its original term were orthogonalized, their VIF scores (1,021 and 1,008 respectively) were acceptable and no further steps were required. However, extremely high multicollinearity (VIF > 150) was found between share of CICs and its interaction term with number of contacts. Even though the existence of this
continue with the analyses without any adjustments. When including interaction effects, the variables that form the basis of the interaction term are per default correlated with the interaction term itself. In such situations, Robinson and Schumacker (2009) “strongly recommend that variables be centered and the variance inflation factor reported otherwise erroneous results could occur and be misinterpreted”. In line with this, share of CICs was mean-centered, reducing the VIF scores for share of CICs and the interaction term to 1,059 and 1,196 respectively. A complete overview of the original and transformed VIF scores can be found in Table 2.
Table 2. VIF-scores before and after mean-centering. Var. VIF-score (original) VIF-score (transformed) Var. VIF-score (original) VIF-score (transformed) 𝑰𝑻𝒊 1,021 1,021 𝑹𝒊 (East) 2,641 2,641 𝑰𝑻𝒊𝟐 1,008 1,008 𝑹 𝒊 (South) 2,952 2,952 𝑵𝑪𝒊 162,280 1,059 𝑺𝑴𝒊 1,391 1,391 𝑪𝑰𝑪𝒊 1,160 1,160 𝑮𝒊 (F) 1,104 1,104 (𝑵𝑪 ∗ 𝑪𝑰𝑪)𝒊 161,859 1,196 𝑰𝑵𝑪𝒊 1,246 1,246 𝑹𝒊 (West) 2,959 2,959 𝑬𝑫𝑼𝒊 1,291 1,291 𝑹𝒊 (North) 2,140 2,140 𝑨𝑮𝑬𝒊 1,158 1,158 4.2. Descriptive Statistics
In order to get a first impression about the content of the dataset, this paragraph will summarize some of the key descriptive statistics. First, the dependent variable and its predictors will be discussed. Subsequently, a brief descriptive breakdown of the demographics will be provided.
Of the 24.001 purchase journeys in the dataset, on average 13,36% leads to customer conversion. 5,21% of which can be allocated to purchases of the focal brand. Thus, about 0,70% of all purchase journeys result in the purchase of a focal brand holiday. Journey length when measured in time falls within the range of 0 seconds (in cases where only one
within a 1 to 8.720 range. On average, customers come into contact with almost 95 touchpoints. 99,06% of these touchpoint contacts are customer-initiated.
In terms of demographics, the group of customers that embarks on these purchase journeys is made up of 57,8% females and 42,2% males. Their average age is just under 52 years old, although ages range from 17 to 94 throughout the dataset. A full overview of the variables in the dataset, their definitions, frequencies, means and standard deviations can be found in appendix A.2. An excerpt of this appendix can be found in Table 3.
Table 3. Excerpt of descriptive statistics from appendix A.2.
Var. M S.D.
Purchase Any 0,13 0,34
Purchase Own 0,01 0,08
Total Journey Time 2.979.227,45 (~ 34 days) 5.304.882,67 (~ 61 days) Intercontact Time 85.579,67 (~ 1 day) 157.947,43 (~ 2 days) Number of Contacts 94,57 273,93 CIC 92,78 267,44 FIC 1,79 22,87 CIC Share 0,99 0,06 Age 51,74 16,06
4.3. Assumptions for Logistic Regression
As was indicated in the methodology section, four formal assumptions underlie logistic regression (Pituch and Stevens 2016).
The first of which is correct specification of the model. Correct specification means (1) selection of the correct link function, (2) inclusion of appropriate predictors only and (3) inclusion of interaction terms when required. The choice for the link function (logit, rather than probit) has already been discussed and relied mostly on mathematical convenience. Appropriate predictor selection primarily focuses on including relevant predictors and excluding irrelevant ones. When doing so, one “should rely on theory, previous empirical work, and common sense to identify important explanatory variables” (Pituch and Stevens 2016, p. 454). The extensive literature review that was performed for this research, combined with the stepwise modeling approach suggested before (Lani 2014), will ensure inclusion of theoretically and statistically relevant variables in the model. Also, the comparison of
to make inferences about the hypotheses. Thirdly, an interaction term is included for the expected moderation effect of share of CICs on the relationship between number of contacts and purchase probability.
The second assumption is about independence of observations. The data that are used in this research are considered to be a reliable representation of the population that considers booking a holiday, according to GfK. However, the data are panel-type, which means that multiple measurements of the same user occur in the dataset, undermining the assumption. By including demographic variables in the model, this research controls for this effect (i.e. multiple measurements of the same respondent will have identical demographic variables and so the bias is counterbalanced).
The third assumption states that the predictors should be measured without (structural) measurement error. It is anticipated that the data collection by GfK is of the highest possible quality and that their expertise in collecting data is sufficient to satisfy this assumption. Finally, a large enough sample size is required for logistic regression. In general, as sample size with less than 100 observations is likely to cause problems, whereas a sample size over 500 – with a minimum of 10 observations per predictor - is oftentimes sufficient (Long 1997). The sample size of this research exists of 24.001 observations and hence meets the requirements.
4.4. Model Selection
In the coming paragraph, multiple model estimations will be discussed and analyzed. The best performing model will form the basis for hypothesis testing. Both to determine the number of control variables to include (considering the missing values in these variables), as well as to adhere to Lani’s (2014) guidelines, stepwise modeling was used to compare multiple models. For the complete estimation results of all models, one is referred to the appendix, where the outputs are presented in Appendix B (B.1 to B.8).
Initially, a model was created with all predictors, but without any control variables (model 1). Afterwards, control variables were added in the same groups as they appear in Table 1. First,
gender was added (model 2) as this variable had most academic literature as back-up.
Afterwards region and size of municipality were added (model 3), followed by age, income and education – resulting in the complete model as specified for this research (model 4). Subsequently, insignificant variables were deleted to assess their impact on the model. As
found to be the least significant variable (p = 0,491). It was hence deleted together with the interaction term for which it was included (p = 0,332). Intercontact time squared was deleted for model 7 as it was least significant in model 6 (p = 0,426). Interestingly, the b-coefficient for the main effect of intercontact time changed drastically when excluding the polynomial term (from -82,11933 to -0,00000). This indicated that more in-depth research into the shape of the relationship of intercontact time might be required. Once the results of the final model were analyzed, intercontact time was assessed in more detail to explain the relationship further. In model 7, the only variable that remained insignificant gender with p = 0,413.
Deleting this variable led to model 8: a model with significant (p < 0,05) or marginally (p < 0,10) significant variables only.
For all eight models, the following four comparison criteria were calculated: Hitrate, Pseudo-R2 (in this case Nagelkerke-R2), Akaike Information Criterion (AIC) and top-decile lift
(TDL).
Hitrate is a synonym for ‘percentage correctly classified’, a very common measure of model accuracy. As the name suggests, it is calculated as a percentage of the total cases that a
specific model can rightly predict (Pituch and Stevens 2016). The higher the hitrate, the better the predictive capability of the model. As has been discussed before, only 13,36% of the purchase journeys led to conversion. Since most of the data exists of ‘no purchase’, it is easy for a model to predict a large number of cases correctly. Moreover, a model that classifies purchases rather than non-purchases correctly, has more practical use. Therefore, separate hitrates were calculated for the percentage of zero’s (no purchase) and one’s (purchase) that each model could classify correctly. Model 4 scores best with an overall hitrate of 86,30% and hitrates of 51,05% and 86,88% for purchases and non-purchases respectively.
In linear regression modeling, it is common to test for the strength of association between the predictors and the independent variable of a model by means of R2. Since the functional form
of logistic regression does not allow for such inferences, a broad range of R2-like measures
has been developed: so called Pseudo-R2’s (Pituch and Stevens 2016). Although these cannot
be interpreted like traditional the R2, a higher Pseudo-R2 does indicate a better model fit. In
this research, Nagelkerke-R2 is employed, on which models 4, 6, 7 and 8 score highest with
11,3%.
Since the six different models are nested versions of each other, Dc2 -tests are inappropriate
desirable (Pituch and Stevens 2016). For this research, the most popular of its kind was used: Akaike Information Criterion (AIC). The best model is the one with the lowest AIC, which in this case is model 8 with an AIC of 12.551.
Finally, the models were also assessed by means of lift curve analysis. Hitrate, Pseudo-R2 and
AIC are more traditional statistical methods, whereas practitioners often measure model performance through summarized descriptive methods like top-decile life (TDL) (Greene and Milne 2010). Including a practically relevant comparer can help deciding on the best model. TDL is a measure of classification quality. Higher scores are considered better and a score of 1 indicates equal classification quality to a random model. All models predict approximately three times better than a random model, with model 2 having the highest TDL of 3,169. The outcomes of the comparison criteria calculations are summarized in Table 4.
Table 4. Model comparison based on hitrate, Pseudo-R2, AIC and TDL.
Model / Test Hitrate
Overall Hitrate 0 Hitrate 1 Nagelkerke R2 AIC TDL
As can be seen in Table 4, the performances of all six models are extremely close. In terms of face validity, no remarkabilities - except for the aforementioned change in the b-coefficient for intercontact time - were detected in or across the models. All parameter estimations remained rather constant throughout the different specifications. Based on the performance comparison in Table 4 and the stability of the parameters across models, the missing values in the control variables do not seem to alter the performance of the models in a negative way. On the other hand, including the control variables also improves the models only marginally, which could hint that including them is superfluous. Considering this specific research and its data, the control variables have an additional benefit in the fact that they compensate for the existence of repeated measurements in the panel-data. These variables thus aid in satisfying the assumption of independence of observation as indicated by Pituch and Stevens (2016). Hence, if they do not weaken the model it would be wise to still include them. In terms of model performance, the complete model (model 4) is best with regard to all three hitrate measurements as well as Nagelkerke R2. Despite the fact that this model includes the most
variables of all estimated models, it also perform very good in terms of AIC, a measure that penalizes for the inclusion of additional parameters. Furthermore, this model includes all control variables, which has the aforementioned benefits with respect to the data type. Only on TDL it scores worst of all models. However, TDL has lower statistical certainty in
assessing model quality than the other methods and might therefore be of lower importance in selecting an appropriate model (Greene and Milne 2010). After careful consideration, it was decided that hypothesis testing was best done with the fourth model, based on the
justification above. A likelihood ratio test confirmed that the fourth model fits the data statistically significantly better than a null-model (p = ,000).
4.5. Hypothesis Testing
The estimation results from model 4 are presented in Table 5. For enhanced interpretability, the odds-ratios (OR) and marginal effects (ME) are presented in the same table as separate columns.
Table 5. Binary logistic regression estimation results (Model 4).
Var. b Std. Error z-value Sig. OR ME
(Intercept) -3,02200 0,20700 -14,602 < ,001 *** 0,0487 𝑰𝑻𝒊 -82,14000 11,20000 -7,332 < ,001 *** <0,01 -8,42300 𝑰𝑻𝒊𝟐 -7,61400 9,65300 -0,789 ,430 0,0004 -0,78080 𝑵𝑪𝒊 0,00185 0,00009 20,794 < ,001 *** 1,0019 0,00019 𝑪𝑰𝑪𝒊 -0,24810 0,39770 -0,624 ,533 0,7803 -0,02544 (𝑵𝑪 ∗ 𝑪𝑰𝑪)𝒊 -0,00128 0,00134 -0,957 ,339 0,9987 -0,00013 𝑹𝒊 (West) -0,06216 0,08787 -0,707 ,479 0,9397 -0,00631 𝑹𝒊 (North) 0,07789 0,10590 0,735 ,462 1,0810 0,00817 𝑹𝒊 (East) -0,01019 0,00908 -0,112 ,911 0,9899 -0,00104 𝑹𝒊 (South) 0,10640 0,00899 1,183 ,237 1,1123 0,01113 𝑺𝑴𝒊 0,04082 0,02063 1,979 ,048 * 1,0417 0,00419 𝑮𝒊 (F) -0,03502 0,04890 -0,716 ,474 0,9656 -0,00360 𝑰𝑵𝑪𝒊 0,12040 0,01630 7,386 < ,001 *** 1,1280 0,01235 𝑬𝑫𝑼𝒊 0,04411 0,01402 3,147 ,002 ** 1,0451 0,00453 𝑨𝑮𝑬𝒊 0,00233 0,00160 1,462 ,144 1,0023 0,00024 Signif. codes: 0 ‘***’ 0,001 ‘**’ 0,01 ‘*’ 0,05 ‘.’ 0,1 ‘ ’ 1
When interpreting the b-coefficients, positive parameters indicate a positive relationship, whereas negative parameters indicate a negative relationship. In other words: A positive (negative) value for b indicates that an increase in that variable increases (decreases) the probability of observing Y=1 (i.e. a customer converses). Similarly, odds-ratios indicate a positive relationship when their values are larger than 1. Values below 1 indicate a negative relationship. As odds-ratios are merely the exponents of the b-coefficients, both present the same results in different formats.
for each additional touchpoint contact. Be aware that marginal effects can differ at other points in the data, because the relationship is logarithmic rather than linear. The marginal effects for each variable reported in Table 5 assume that the other covariates are at their average value.
The first hypothesis expects an inverted U-shaped relationship between the average
intercontact time and an individual’s purchase probability, meaning that shorter intercontact time initially increases purchase probability, after which the effect diminishes. The main effect 𝐼𝑇" is highly statically significant (b = -82,14000; SE = 11,20000; p = < ,001). The directions of the b-parameter, the odds ratio (<0,01) and the marginal effects (-8,42300) are extremely negative, indicating that increased intercontact time decreases purchase
probability. Besides, the quadratic effect 𝐼𝑇"> is statistically insignificant (b = -7,61400; SE =
9,65300; p = ,430). Consequently, no evidence for a quadratic effect can be established from the data. In conclusion, only very limited support is found for hypothesis 1. A graphical representation of the logistic regression curve for intercontact time and its second order polynomial can be found in Appendix C.2.
For the second hypothesis, a positive relationship was anticipated between the number of touchpoint contacts in the purchase journey and purchase probability. Positive and significant signs are found for 𝑁𝐶" in the model (b = 0,00185; SE = 0,00009; p = < ,001), as is also indicated by OR = 1,0019 and ME = 0,00019. In other words, for every additional touchpoint contact in a customer’s purchase journey, the likelihood that he/she actually purchases a product increases with 1,0019 times. Hypothesis 2 is hence fully supported. A graphical representation of the logistic regression curve for number of contacts can be found in Appendix C.4.
The third hypothesized relationship was a positive interaction effect between the share of customer-initiated contact with the number of touchpoint in the customer journey. The main effect (b = -0,24810; SE = 0,39770; p = ,533) and the interaction effect (b = -0,00128; SE = 0,00134; p = ,339) are insignificant. Therefore, hypothesis 3 is not supported.
4.6. Model Re-estimations
In order to further explore the hypotheses that were not (fully) supported, the logit model was re-estimated multiple times with some adjustments.
(b = -0,35871; SE = 0,37068; p = ,333). Although the p-value decreased from p = ,533 to p = ,333, the main effect remained statistically insignificant. No direct effect of share of CICs on individual purchase probability was found (see Appendix D.1 for the complete estimation results).
Afterwards, the original model was applied to two separate subsets of the data: One including only CICs and the other including only FICs. By doing this, the effect of average intercontact time and number of contacts could be distinguished for both forms of contact. Since one subset existed of only CICs and the other of only FICs, the variable share of CICs was excluded from these estimations together with the interaction term; all other variables were included. The estimation results for both models are presented in Table 6 (CIC-only) and Table 7 (FIC-only).
Most results are comparable to the results in Table 5: Both in the CIC-only dataset (b = 0,00189; SE = 0,00009; p = <,001) and the FIC-only dataset (b = 0,00411; SE = 0,00128; p = <,001) a significant positive relationship is found between the number of touchpoint contacts and purchase probability. This finding reconfirms hypothesis 2. Also, the size of the b -coefficients for number of contacts aligns with the initial finding that hypothesis 3 is unconfirmed. In fact, the effect of is larger in the FIC dataset (b = 0,00411) than in the CIC dataset (b = 0,00189). This contradicts the theoretical framework developed for hypothesis 3, which stated that each customer-initiated contact would be of more influence on purchase probabilities than each firm-initiated contact.
Table 6. Binary logistic regression re-estimation results (CIC-only subset)
Var. b Std. Error z-value Sig. OR ME
(Intercept) -3,20000 0,20740 -15,424 < ,001 *** 0,0408 𝑰𝑻𝒊 -99,78000 13,86000 -7,201 < ,001 *** <0,001 -10,20100 𝑰𝑻𝒊𝟐 -11,31000 11,77000 -1,113 ,266 <0,001 -1,33970 𝑵𝑪𝒊 0,00189 0,00009 21,035 < ,001 *** 1,0019 0,00019 𝑹𝒊 (West) -0,06269 0,08781 -0,714 ,475 0,9392 -0,00634 𝑹𝒊 (North) 0,07830 0,10580 0,740 ,459 1,0814 0,00819 𝑹𝒊 (East) -0,01282 0,09074 -0,141 ,888 0,9873 -0,00131 𝑹𝒊 (South) 0,10800 0,08986 1,202 ,229 1,1141 0,01127 𝑺𝑴𝒊 0,04163 0,02061 2,020 ,043 * 1,0425 0,00426 𝑮𝒊 (F) -0,03316 0,04888 -0,678 ,498 0,9674 -0,00339 𝑰𝑵𝑪𝒊 0,12120 0,01631 7,431 < ,001 *** 1,1288 0,01239 𝑬𝑫𝑼𝒊 0,04317 0,01400 3,083 ,002 ** 1,0441 0,00441 𝑨𝑮𝑬𝒊 0,00243 0,00160 1,526 ,127 1,0024 0,00025 Signif. codes: 0 ‘***’ 0,001 ‘**’ 0,01 ‘*’ 0,05 ‘.’ 0,1 ‘ ’ 1
Table 7. Binary logistic regression re-estimation results (FIC-only subset)
Var. b Std. Error z-value Sig. OR ME
Two new models were estimated to gain further insights in the shape of 𝐼𝑇". First of all, a model was estimated excluding 𝐼𝑇"> (see Appendix D.2 for the complete estimation results).
Similar to what was detected during the model selection process, the b-coefficient for the main effect of intercontact time changed to -0,00000 (SE = 0,00000; p = <,001). Next, a third-order polynomial (i.e. 𝐼𝑇"?) was added to the original model to obtain more knowledge
on the existence of any higher-order curvilinearity (Appendix D.3). The estimation results show that the third-order polynomial is highly significant with a positive sign (b = 20,12000; SE = 5,79100; p = <,001). The main effect parameter is again significant and highly negative (b = -79,04000; SE = 8,25000; p = <,001). The second-order polynomial stays insignificant although its estimate changes from negative to positive (b = 8,94700; SE = 6,09700; p = ,142).
Overall, the estimates, odds-ratios and marginal effects for intercontact time are either extremely large or extremely small. Also, the direction of the effect is dependent on the number of polynomials included. Accordingly, the results indicate curvilinearity that cannot effectively be captured in polynomial extension of the binary logistic model. This is
Table 8. Binary logistic regression re-estimated model performance overview.
Re-estimation / Test Hitrate Overall
Hitrate 0 Hitrate 1 Nagelkerke
R2 AIC TDL Re-estimation 1 Excluding (𝑁𝐶 ∗ 𝐶𝐼𝐶)" 86,34% 86,84% 49,35% 0,113 12.554 2,993 Re-estimation 2 CIC-only data 86,29% 86,83% 47,84% 0,112 12.561 2,981 Re-estimation 3 FIC-only data 76,68% 76,80% 68,75% 0,077 1.135 2,093 Re-estimation 4 - 𝐼𝑇"> 86,38% 86,88% 51,05% 0,113 12.554 2,993 Re-estimation 5 + 𝐼𝑇"? 86,38% 86,88% 51,05% 0,114 12.547 2,984
4.7. Generalized Additive Model
To evaluate the form of the relationship between intercontact time and individual purchase probability further, other, more exploratory statistical techniques may help. A very useful tool to find out the shape of a relationship is Generalized Additive Modeling, a flexible, semi-parametric extension of GLM (McCullagh and Nelder 1989). GAM allows the data to select the functional form freely, rather than limiting itself to specific pre-determined distributions (Jones and Almond 1992). Hence, it is considered a more useful technique for data
exploration than GLM (Yee and Mitchell 1991). Because the model is additive, inferences about individual covariates can only be made if no interaction effects are present (Yee and Mitchell 1991). Accordingly, a Generalized Additive Model (GAM) was estimated without the interaction term and with intercontact time as a smooth term (‘GAM 1’). The other
independent variables were included as regular parametric coefficients (Appendix E.1). GAM allows the modeler to choose which variables to include as smooth variables and which ones as parametric parameters. For comparison purposes, a model was estimated (‘GAM 2’) where the continuous variables intercontact time, share of CICs and Age were included as smooth terms and all other terms as regular parametric coefficients (Appendix E.2). Number of contacts was not included as a smooth, as this variable is assumed to be parametric
factors were insignificant (Appendix E.3). The last insignificant variable (i.e. gender) was dropped afterwards to create GAM 4 (Appendix E.4).
The models were compared on AIC, adjusted R2 and Generalized Cross Validation (GCV). GCV is a selection criterion similar to AIC, in the sense that it focuses on minimized model prediction error. Like with AIC, a lower score indicates a better model. An overview of the comparison criteria for the models can be found in Table 9. GAM 4 performs best on AIC (although only marginally better than the GAM 2 and GAM 3) and is most parsimonious. In terms of R2, GAM 2 performs (slightly) better than the others. However, since the differences in model performance are so small, all models suffice for the purpose of this analysis. As it is the most parsimonious model, GAM 4 was chosen as the basis to evaluate the relationship of intercontact time.
Table 9. Generalized Additive Model comparison based on AIC, R-squared and GCV.
Model / Test AIC R2 (adj.) GCV
GAM 1 10.045 0,109 0,105
GAM 2 10.526 0,111 0.105
GAM 3 10.525 0,110 0,105
GAM 4 10.524 0,110 0,105
In models with smooth terms, issues may arise with concurvity: the non-parametric equivalent of multicollinearity. Presence of concurvity can lead to wrong statistical
interpretations and overstatement of significance (Ramsay, Burnett, and Krewski 2003). A test for concurvity revealed no alarming scores (scores leaning towards 1 are considered troublesome). An overview of the outcomes of the concurvity test for the fourth model can be found in Table 10.
Table 10. Generalized Additive Model concurvity test results (model 4).
s(𝑰𝑻𝒊) s(𝑪𝑰𝑪𝒊) s(𝑨𝑮𝑬𝒊)
Worst 0,17 0,05 0,15
Observed 0,15 0,01 0,07
Estimate 0,01 0,01 0,10
Since the area of interest is a smooth parameter (i.e. intercontact time), the bottom block deserves special attention. The presented parameters are the effective degrees of freedom (‘edf’), the reference degrees of freedom (‘Ref.df’), the F-value and the p-value (‘Sig.’). Together, the F-value and Sig. column indicate the significance of the parameter. It can be concluded that the smooth term s(𝐼𝑇") is highly significant (p = ,000). The reference degrees
of freedom are those used to estimate the parameters, whereas the effective degrees of freedom indicate the degree of (non-)linearity (higher edf scores equal less linearity). The results show that intercontact time is highly non-linear (edf = 56,65). In order to assess the actual shape of the relationship, graphical analysis is required. The GAM plot for intercontact time is displayed in Figure 3 and shows a gradually declining curve that peaks heavily at around 10.000 seconds (see detailed plot from 0 to 50.000 seconds in Appendix. E.5). The plot clearly shows a non-linear relationship with a single optimal point. Intercontact times that are both shorter and longer than this optimal point lead to a relative decrease in purchase probability. The GAM plots for the smooth terms for share of CICs and age can be found in Appendix. E.6. These plots resemble linearity to a much larger extent, as was to be expected from their edf scores (edf = 2,39 and edf = 3,88) respectively. Furthermore, the positive and significant effect of number of contacts is similar under both the GLM and GAM estimation, reinforcing the earlier findings regarding the confirmation of the second hypothesis.
Table 11. Generalized Additive Model estimation results (model 4). Parametric Coefficients
Var. Est. Std. Error t-value Sig.
(Intercept) 0,03402 0,01216 2,798 0,005 ** 𝑵𝑪𝒊 0,00020 0,00001 19,768 0,000 ***
𝑺𝑴𝒊 0,00352 0,00188 1,876 0,061 .
𝑰𝑵𝑪𝒊 0,01114 0,00174 6,415 0,000 ***
𝑬𝑫𝑼𝒊 0,00504 0,00152 3,310 0,001***
Approximate Significance of Smooth Terms
Var. edf Ref. df F-value Sig.
s(𝑰𝑻𝒊) 56,65 68,33 12,912 0,000 ***
s(𝑪𝑰𝑪𝒊) 2,39 2,96 3,377 0,014 *
s(𝑨𝑮𝑬𝒊) 3,88 4,82 4,148 0,001 **
