Choice modelling in marketing-some examples

Hans S. Solgaard, Department of Environmental and Business Economics

June 2008

Overview

a. What is marketing?

b. The complexity of the choice context in marketing

c. Brief history of choice models in marketing.

d. Some marketing examples -Choice of TV program -An integrated model of purchase incidence, brand choice and quantity decisions -A model of store choice

Marketing

Because the purpose of business is to create and keep customers it has only two central functions – marketing and innovation. The basic function of marketing is to attract and retain customers at a profit

(P. Drucker; 1999).

Therefore:

It is one of the most important areas of research in marketing to understand and measure the effects of consumer/customer choice

Complex choice context

-many choice alternatives

-high number of attributes, features and characteristics to to characterize alternatives and decision makers.

-consumers are heterogenous

Brief historyDespite the complexity of consumer choice the choice modelling literature was dominated by fairly simple stochastic brand choice model until beginning of the 80s.

- parsimonious in behavioral assumptions and in parameterization.

- contains no decision variables

Brief historyMost widely used models:

-The NBD (negative bionomial distribution) model Purchase incidence described by Poisson process (memoryless process!?) Heterogeniety modelled by Gamma distribution.

-The Multinomial-Dirichlet model.

-Beta-bionomial model.

-Linear learning model.

Brief history

BIG BANG in choice modelling was the development of the random utility model formulated as a multinomial logit model by McFadden et al. (1973).

An initial appeal of the MNL model was due to it being stochastic and yet admitting decision variables like price, quality, promotion etc.

Utility directly incorporated in the model. Utility specified as a stochastic function consisting of deterministic component and a random component.

Example ”A model of audience choice of local TV news program” Solgaard (1979, 1984)

The model provides:

a description of the associative relationship between viewers’ actual choices of news programs on the one hand and attributes of the programs on the other. I derive this model from a model of individual viewer choice behavior that specifies a viewer’s probability of choosing a particular program on a given occasion as a function of the viewer’s relative preference toward that program. The audience model is operationalized using a multinomial logit model.

ExampleExamples of factors that may influence the choice decision:

(1) news program attributes such as cast members (anchorman, weatherman,

sportscaster), program contents, the sequence of presentation of the various program segments, photographic coverage, scheduling (i.e., time of day the program is offered) and adjacent programs);

(2) the general image of the TV station;

(3) the quality of TV reception;

(4) the news of the day.

ExamplePreference towards a news program:

uji = Aji + Sji, j=1,2 ... J,

where

uji = measure of preference assigned to program j by individual i,

Aji = measure of individual i’s attitude toward program j,

Sji = unobserved random component,

J = number of alternative local TV news programs.

ExamplePreference of an arbitrary viewer may be written as:

ExampleAttitude towards a news program is specified in the form of a multi-attribute attitude model:

ExampleThe preference function can then be specified as:

The event that an arbitrary viewer will choose program j

ExampleAssuming the random terms follow the Type I Extreme Value Distribution results in the MNL model:

Example, results.

Economic models of choiceAssume the existence of a scalar measure of consumer utility that can be used to generate a preference ranking of the choice alternatives.

Consumers are assumed to make choices that are consistent with the concept of constrained utility maximization:

max u(q), subject to p´q ≤ y

Where x denotes a vector of quantities, p denotes the price of each item and y is the budget constraint (i.e. the max expenditure a consumer is willing to make in a product category)

Example An integrated model of purchase incidence, brand choice and purchase quantity, (Chiang, 1991 and Chintagunta, 1993, also see Hanemann, 1984)

-Focuses on a single product category.

-Shopping basket separated into two groups: one containing the product category of interest, the other all other goods purchased. All other goods are treated as a composite good. The composite good is assumed essential and therefore always bought.

-Consumers/households make decisions based on product attributes. A consumer’s (subjective) evaluation of each brand in the category is summarized in an index, ψ, - a function of product attributes, marketing mix variables and consumer characterisitcs.

ExampleConsider a store visit at time t, - made by household i. Where j refers to brand j. The household’s problem is to maximize u subject to the budget constraint:

subject to:

Where z is the composite good.

ExampleTwo possible solutions:

a. Non-purchase with the budget spent entirely on the composite good, and

b. Brand choice and quantity demanded.

Solution: Non-purchase if the reservation price/shadow price, say R, is below the quality adjusted prices for the brands in the considered category.

R < pj/ψj for all j

Purchase if the reservation price/shadow price, say R, is above the quality adjusted price for at least one of the brands in the category.

R > pj/ψj and R < pk/ ψk k≠j

Explicit specification of the functional forms for u, ψ and the distribution for ε are of course requisite for empirical applications.

ExampleExplicit specification of the functional forms for u, ψ and the distribution for ε are of course requisite for empirical applications.

Specifications:

u may be specified as the indirect translog utility function.

Ψ may be given the form:

exp(aij + Σxijtsβs + εijt)

Where aij represent hh i’s intrinsic preference for brand j, xijts is the value of

the sth quality attribute af brand j for hh i on store visit t, and βs the associated parameter.

These specifications leads to flexible and useful models for each of the choice decisions, for the brand choice it results in the MNL.

Store format choice exampleSolgaard and Hansen (2003)

Objective:

(1)To model the store choice decision of supermarket

shoppers so as to be able to investigate the sensitivity of

the store choice decision to changes in shopper’s

perceptions of the choice determinants.

(2) to discuss problems involved in operationalizing

store choice models, using the framework of the

multinomial logit model, and to suggest alternative

model specifications to remedy the identified problems

ExampleDeterminants of store choice:

-Store image i.e. perceptions of store values: Quality/service level

Price level

Samples

Assortment

Accessibility

-Distance

-HH descriptors

Example Store choice

Probability that consumer i will select store format j on a particular purchase occasion:

Example Store choice

Problems with the standard logit model.

1. The coefficients of variables that enter the model are assumed to be same for all consumers.

2. The standard logit exhibits the IIA (independence from irrelevant alternatives) property.

A random coefficients logit model can remedy these problems.

Example Store choice

Operationalization of the store choice model as a random coefficients logit model:

Where Xij is a vector of observed store attribute perceptions and household descriptors and βij is a vector of unobserved coefficients for each hh that varies randomly over the households according to a distribution G. The term eij is an unobserved random term independent of X and β, and distributed IID Type I extreme value.

Example store choice

Since eij is IID extreme value, as in the standard logit model

We estimate the model applying Bayesian estimation.

Example Store choice, results

References:Chiang, J. (1991), A Simultaneous approach to the whether, what and how much to buy

questions, Marketing Science, vol. 10, no. 4, pp 297-315

Chintagunta, P. K., (1993), Investigating purchase incidence, brand choice and purchase quantity decisions of households, Marketing Science, vol. 12, no. 2, pp 184-208

Hanemann, W.M. (1984), Discrete/continous models of consumer demand, Econometrica, vol. 52, no. 3, pp 541-561.

Solgaard, H.S. (1979), Modelling choice of local TV news program, Unpublished Ph.D. dissertation, Graduate School of Business and Public Administration, Cornell University, Ithaca NY.

Solgaard, H.S. (1984), A model of audience choice of local TV news program, International Journal of Research in Marketing, pp 141-151.

Solgaard, H.S. and T. Hansen (2003), A hierarchical Bayes model of choice between supermarket formats, Journal of Retailing and Consumer Services, vol. 10, pp 169-180.