Marketing (Statistics) and Applied Probability Models

The success of the marketing function within an organization is key to the success of the organization as a whole. Mathematical models can help marketers answer questions about marketplace needs and buyer behavior by providing a mathematical representation of the system or situation being studied. Despite the fact that the real world is an infinitely complex entity, models should still strive to be succinct and parsimonious. Empirical observations in combination with a review of the literature will give the analyst a good starting point from which to decide which variables to include or exclude in the model building process. There are a number of approaches available to help analysts determine which variables will be most predictive in a model. Marketing models can be used in a wide variety of situations. Three of these include the determination of customer lifetime value, optimizing sales force deployment, and optimizing the mix between expert judgment and statistical technique in building the best model for direct marketing.

Dr. Ruth A. Wienclaw holds a doctorate in industrial/organizational psychology with a specialization in organization development from the University of Memphis. She is the owner of a small business that works with organizations in both the public and private sectors, consulting on matters of strategic planning, training, and human/systems integration.

Keywords Buyer Behavior; Consumer; Customer Lifetime Value; Customer Relationship Management; Dependent Variable; Empirical; Forecasting; Marketing; Model; Probability; Regression; Stochastic; Variable

Statistics > Marketing (Statistics) & Applied Probability Models

Overview

The success of the marketing function within an organization is key to the success of the organization as a whole. Marketing involves creating, communicating, and delivering value to consumers in ways that benefit the organization and its stakeholders. In addition, modern marketing theory emphasizes customer relationship management, the process of identifying prospective customers, acquiring data concerning these prospective and current customers, building relationships with customers, and influencing their perceptions of the organization and its products or services. Because of the importance and the complexity of these tasks, many marketing departments rely on the use of mathematical models to help them forecast buyer behavior under various sets of variables and "what if" scenarios. Marketing is concerned with both the description of actual, observed behavior and the prediction of future behavior. For example, one might be interested to know why customers prefer a widget over a gizmo. One might also be interested to know whether customers might prefer a gizmo if it were redesigned to improve certain characteristics. Mathematical models can help marketers answer these questions by providing a mathematical representation of the system or situation being studied.

Despite the fact that the real world is an infinitely complex entity, models should still strive to be succinct and parsimonious. The state of modeling science is such that it can only take into account a finite amount of variables. It is part of the modeler's task to determine which variables should and should not be included in the model-building process. In general, this means considering only those things that are relevant to the central research question. For example, if one is interested in predicting if a proposed turquoise widget will appeal to women, the question could be broken down according to infinite demographic variables such as age range, education, area of the country, national origin, and whether or not they were cat lovers. Although these variables may have some effect on prospective customers' decision to purchase the new widget, they are less relevant to the central question concerning women and the color turquoise and should, therefore, probably be eliminated from the model unless they are theorized to be central to the question at hand. A good model needs to have both fit (i.e., accurately models the real world situation) and robustness (i.e., accurately predicts future behavior). A model that attempts to consider all observations usually predicts poorly or yields predictions that are too ambiguous to be of much practical use. To achieve stronger predictions, one must often compromise and predict fewer situations. The best models make the appropriate compromise between predicting in all circumstances and predicting accurately. Anything else will not have much applicability. Two well-known and established statistical techniques used in mathematical modeling for market analysis are conjoint analysis and the Dirichlet model.

Empirical observations in combination with a review of the literature will give the analyst a good stating point from which to decide which variables to include or exclude in the model building process. Typically, theorists and researchers will have given serious thought to the relationship between variables, and the literature will express the state-of-the-art thinking about various aspects of the universe of data at which one is looking and will have built upon previous research and models. Similarly, empirical observations of trends and relationships by the marketing personnel or management in the organization can lead to other strong assumptions that are good points of departure for building a model of buyer behavior. However, strong assumptions alone are insufficient: To be useful, a model also needs to be testable. Models are only of use if they have validity and reliability. Validity means that the model accurately predicts what it is intended to predict. Reliability means that the model consistently measures what it is intended to measure. A model cannot be valid unless it is reliable.

There are a number of approaches to selecting variables for marketing models:

• Forward Selection Approach
• Backward Elimination Approach
• Stepwise Approach
• R-squared Approach
• Rule of Thumb Approach

Forward Selection Approach

The forward selection approach adds variables to the model until no variable that adds significance to the model is not incorporated into it. As each variable is added to the model, a test statistic is first calculated to determine the variable's contribution to the model. If the test statistic is greater than a predetermined value, it is added to the model; if the test statistic is less than the predetermined value, it is not added. This process is completed for each potential variable of interest until the model is populated with all variables that make a significant contribution to the model.

Backward Elimination Approach

Whereas the forward selection approach starts with an empty model and adds variables to it, the backward elimination approach starts with a model fully populated with all potential variables and then subtracts those that do not add significance to the model. As with the forward selection approach, the backward elimination approach ends with a model in which all the included variables have a test statistic that is greater than the predetermined value.

Stepwise Approach

A third approach to selecting variables is the stepwise approach, which is a variation of the forward selection method. As opposed to the forward selection approach, however, in the stepwise approach, not all the variables already in the model necessarily remain in it. As in the forward selection approach, variables are added one at a time after being tested with the test statistic. However, the stepwise also examines the variables already included to delete any that do not have a test statistic value greater than the predetermined number.

R-squared Approach

A fourth approach to variable selection is the R-squared approach. This approach is used to find multiple subsets of variables that best predict the dependent variable using an appropriate test statistic. This approach can be used to find the best one-variable model, the best two-variable model, and so forth.

Rule-of-Thumb Approach

Another approach is the Rule-of-thumb approach. This approach selects the variables best associated to the dependent variable as determined by the Pearson correlation coefficient r. The variables are then ranked by their r values and the top k (as predetermined) ranked variables are included in the model. If a regression model with these variables demonstrates that all the variables have test statistic values greater than the predetermined value, then the set is determined to be the best.

Although it is important to choose the right variables for building a model, it is also important to remember that models are not set in stone. Model building is an iterative process and a model that does not meet the tests of validity and reliability can be refined to better model the real world. Indeed, the factors influencing customer behavior change over time and the marketing model needs to be flexible to reflect those changes. Based on empirical observation, expert judgments, and the insights of the literature, one posits a theory and develops a model based on its assumptions. The model is then tested against the real world and modified to better reflect the real world experience. This process is repeated as necessary until the model reaches the desired level of accuracy.

Similarly, it is also important to remember that the needs of the marketplace are not static. For example, in the mid-1950s, grocery stores stressed having all the ingredients available that the homemaker needed to make meals from scratch. At that time, frozen dinners were almost unheard of. Today, however, many people are more concerned with convenience and less people cook from scratch. As a result, grocery stores today offer a wide array of frozen foods that can be popped into a microwave oven or prepared meals that can be easily cooked or reheated and served with a salad from the salad bar. The marketing model that was appropriate for the mid-20th century grocery store is no longer appropriate in the 21st century.

Applications

Marketing models can be used in a wide variety of situations. Three of these are the determination of customer life time value, optimizing sales force deployment, and optimizing the mix between expert judgment and statistical technique to build the best model for direct marketing.

One of the reasons that many marketing departments turn to modeling is because of the complexities of customer relationship management. Marketing departments strive not only to win the customer for a one-time purchase, but to gain customer loyalty to the business or brand and thereby win continuing sales over the long term. In customer relationship management, the business identifies prospective customers, acquires data concerning prospective and current customers, builds relationships with customers, and attempts to influence their perceptions of the organization and its products or services. However, it would be impossible to perform this function for all possible customers; so, many marketing departments tend to cultivate deeper relationships with those customers who will spend more money with a business or brand over the course of their lifetimes. This concept is called customer lifetime value. This information theoretically allows a business to know how much each customer is worth in terms of dollars of income which, in turn, allows businesses to better know how to spend their marketing budget. For example, if the 20-35 year old demographic will potentially spend ten times as much money on widgets during their lifetime than the 60-75 year old demographic, most businesses would place more marketing effort on the younger demographic. However, calculating customer lifetime value tends to be complex (e.g., the customer's need or desire for the product may change, the competition may bring out a product that better fits the customer's needs), and reliable data to build a usable model and net cash flow from the customer are difficult to gather. Haenlein and Libai (2013) highlight the benefit of targeting customers with high lifetime value, also known as "revenue leaders." The authors argue that targeting revenue leaders can create high value by accelerating adoption among these customers and because of the greater-than-average value that revenue leaders generate by influencing other customers with similarly high lifetime value.

Although knowing how much the "average" customer will spend on a company's products over the course of his/her lifetime is of interest in general, it is particularly where markets are mature and there is significant competition. This situation is a good example of how mathematical marketing models can be of use. Berger and Nasr (1998) present a series of five general marketing models of customer lifetime value. The simplest of these models assumed one sale per customer a year with both the cost of marketing efforts to retain customers and their actual retention rate remaining constant over time. The second generic model removed the assumption of once-yearly sales and allowed examination of time periods both longer and shorter than one year. The third and fourth models examined the effects of gross contribution margin and promotion costs that vary over time. The final model was based on the assumption of a shrinking customer base in which customers are lost over time and treated as new customers when they return. All these models can be used by marketers for a variety of purposes including making decisions concerning the allocation of marketing dollars for advertising campaigns and forecasting the effect of a marketing strategy particularly vis a vis acquisition and retention of customers and the associated costs and tradeoffs.

Another area in which mathematical models can be useful for marketing is sales force management. This is the process of efficiently and effectively making sales through the planning, coordination, and supervision of others. The sales manager must make the best use possible of both the human and financial resources available to sell the organization's goods and services to potential customers. Sales managers must determine how best to use the resources available to optimize the effectiveness and efficiency of the sales force as a whole. This requires understanding numerous variables and their interactions including the qualifications, abilities, and experience of the sales force as well as the target market and its demographics, needs, and motivations. Data on sales force capabilities and prospective customer needs can be used in the development of a model that allows the sales manager to leverage the strengths of the individual sales personnel and enables each to reach his/her optimal sales potential.

The activities of sales management include recruiting and selecting sales personnel, enabling the sales force to sell (e.g., training, print materials or samples), supervising and coordinating sales efforts (e.g., assigning territories or routes), and other motivating and human resource activities. Deploying a sales force requires simultaneously solving four interrelated problems:

• Determining the size of the sales force needed (i.e., how many sales persons are needed within a territory)
• Determining the optimal location for sales personnel (i.e., how many sales persons are needed within a given sales coverage unit)
• Aligning sales territories (i.e., how best to group sales coverage units into larger geographic clusters)
• Allocating sales resources (i.e., how best to allocate sales personnel time within the coverage units).
• Drexl & Haase (1999) used a nonlinear mixed-integer programming model to solve all four problems simultaneously. They used approximation methods that could solve large scale, real world instances. These methods also provided lower bounds for the optimal objective function value and were benchmarked against upper bounds. The model has been successfully used to manage the sales force of a beverage company in Germany.

Although mathematical models are important tools for developing marketing models, the understanding of applied probability and stochastic processes is insufficient for developing a robust model. For example, one of the problems with these approaches to selecting variables is that they do not identify structure in the data. When building models, the insights of an experienced marketer who understands the parameters affecting buyer behavior can be invaluable. Such expert judgment is essential for the development of a model that realistically models the marketplace and includes all significant variables. The incorporation of human judgment and statistical models can lead to better models.

Morwitz & Schittlein (1998), for example, found that the combination of management judgment and statistical models can lead to increased effectiveness of marketing models. In fact, a model based on this combination of inputs was able to increase profits by more than ten percent. Management decisions are based on a rich history of experience and insight that is often not quantifiable. Attempting to replace managerial insights with a mathematical model ignores a very rich source of information. On the other hand, mathematical modeling can better account for a wider range of data and deal with large amounts of data better than can human beings in most situations. Therefore, it is important to include both mathematics and judgments in the model building process.

However, mathematical modeling is not appropriate for every marketing situation. Not only are mathematical models expensive to develop; in some instances, there are insufficient data to apply to quantitative techniques. Even when sufficient data are available, humans still must decide which variables to include in the analysis and must interpret also the results of the forecast. Therefore, no matter how rigorously a model is developed, judgment is still key to determining which data are relevant to the model. Expert judgments can be helpful in understanding the situation and giving the manager insight into the parameters in which the data and subsequent analysis should be interpreted (e.g., "given the current economy and our market plan, we expect widget sales to rise by two percent over the next quarter"). As a result, quantitative and qualitative analyses are both indispensable for model building.

Terms & Concepts

Buyer Behavior: The complex processes by which consumers choose, acquire, use and dispose of goods and services in order to fulfill their needs and desires.

Consumer: A person or organization that acquires goods or services for direct use rather than for resale or use in a manufacturing process.

Customer Lifetime Value: An estimate of how much a customer will spend with a business or brand during the period when s/he purchases from that business or brand. Analysis of customer value should include consideration of the depth, breadth, and duration of the customer's relationship with the business or brand as well as the cost to acquire, serve, and retain each customer.

Customer Relationship Management: The process of identifying prospective customers, acquiring data concerning these prospective and current customers, building relationships with customers, and influencing their perceptions of the organization and its products or services.

Dependent Variable: The outcome variable or resulting behavior that changes depending on whether the subject receives the control or experimental condition (e.g., a consumer's reaction to a new cereal).

Empirical: Theories or evidence that are derived from or based on observation or experiment.

Forecasting: In business, forecasting is the science of estimating or predicting future trends. Forecasts are used to support managers in making decisions about many aspects of the business including buying, selling, production, and hiring.

Marketing: According to the American Marketing Association, marketing is "an organizational function and a set of processes for creating, communicating and delivering value to customers and for managing customer relationships in ways that benefit the organization and its stakeholders." (http://www.marketingpower.com/content24159.php)

Model: A representation of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. Mathematical or computer models are mathematical representations of the system or situation being studied.

Probability: A branch of mathematics that deals with estimating the likelihood of an event occurring. Probability is expressed as a value between 0 and 1.0, which is the mathematical expression of the number of actual occurrences to the number of possible occurrences of the event. A probability of 0 signifies that there is no chance that the event will occur and 1.0 signifies that the event is certain to occur.

Regression: A statistical technique used to develop a mathematical model for use in predicting one variable from the knowledge of another variable.

Stochastic: Involving chance or probability. Stochastic variables are random or have an element of chance or probability associated with their occurrence.

Variable: An object in a research study that can have more than one value. Independent variables are stimuli that are manipulated in order to determine their effect on the dependent variables (response). Extraneous variables are variables that affect the response but that are not related to the question under investigation in the study.

Bibliography

Berger, P. D. & Nasr, N. I. (1998). Customer lifetime value: Marketing models and applications. Journal of Interactive Marketing, 12, 17-30. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=348356&site=ehost-live

Drexl, A. & Haase, K. (1999). Fast approximation methods for sales force deployment. Management Science, 45, 1307-1323. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=2510404&site=ehost-live

Guyon, H., & Petoit, J. (2011). Market share predictions. International Journal of Market Research, 53, 831-857. Retrieved November 5, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=67274334&site=ehost-live

Haenlein, M., & Libai, B. (2013). Targeting revenue leaders for a new product. Journal of Marketing, 77, 65-80. Retrieved November 5, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=67274334&site=ehost-live

Ho, T. H., Lim, N., & Camerer, C. F. (2006). Modeling the psychology of consumer and firm behavior with behavioral economics. Journal of Marketing Research, 43, 307-331. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=21945242&site=ehost-live

Keon, J. W. (1991). Point of view: Understanding the power of expert systems in marketing - when and how to build them. Journal of Advertising Research, 31, 64-71. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9202171002&site=ehost-live

McCabe, J., Stern, P., & Dacko, S.G. (2012). The power of before and after. Journal of Advertising Research, 52, 214-224. Retrieved November 5, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=77276980&site=ehost-live

Morwitz, V. G. & Schmittlein, D. C. (1998). Testing new direct marketing offerings: The interplay of management judgement and statistical models. Management Science, 44, 610-628. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=812933&site=ehost-live

Ratner, B. (2001). Finding the best variables for direct marketing models. Journal of Targeting, Measurement & Analysis for Marketing, 9, 270-296. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=6614028&site=ehost-live

Shugan, S. M. (2002). Marketing science, models, monopoly models, and why we need them. Marketing Science, 21, 223-228. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=17463152&site=ehost-live

Wyner, G. A. (2006). Why model? Marketing Research, 18, 6-7. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=20577118&site=ehost-live

Suggested Reading

Hanssens, D. M. Leeflang, P. S. H. & Wittink, D. R. (2005). Market response models and marketing practice. Applied Stochastic Models in Business & Industry, 21(4/5), 423-434. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=18071428&site=ehost-live

Hardey, M. (2012). New visions: capturing digital data and market research. International Journal of Market Research, 54, 159-161. Retrieved November 5, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=74637375&site=ehost-live

Ho, T. H., Lim, N., & Camerer, C. F. (2006). How "psychological" should economic and marketing models be? Journal of Marketing Research, 43, 341-344. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=21945228&site=ehost-live

Lodish, L. M. (2001). Building marketing models that make money. Interfaces, 31, S45-S55. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5674823&site=ehost-live

Tian, K. T. & McKenzie, K. (2001). The long-term predictive validity of the consumers' need for uniqueness scale. Journal of Consumer Psychology, 10, 171-193. Retrieved July 19, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=4437050&site=ehost-live