Modeling Buy/No Buy Decisions: a Comparison of Two Methods

ABSTRACT - The decision making process for some products can be characterized as a determination of whether individual brands are acceptable for purchase rather than a search for the optimal brand within a set. For firms with such products modeling demand with tasks that force comparisons among competing products may not be appropriate. This paper contrasts the results of demand estimates that do and do no not require explicit comparisons and-finds that each has a unique but complementary role in modeling demand.

Citation:

Joel Huber and Andrew L. Czajka (1982) ,"Modeling Buy/No Buy Decisions: a Comparison of Two Methods", in NA - Advances in Consumer Research Volume 09, eds. Andrew Mitchell, Ann Abor, MI : Association for Consumer Research, Pages: 357-362.

Advances in Consumer Research Volume 9, 1982      Pages 357-362

MODELING BUY/NO BUY DECISIONS: A COMPARISON OF TWO METHODS

Joel Huber, Duke University

Andrew L. Czajka, Survey Data Research

ABSTRACT -

The decision making process for some products can be characterized as a determination of whether individual brands are acceptable for purchase rather than a search for the optimal brand within a set. For firms with such products modeling demand with tasks that force comparisons among competing products may not be appropriate. This paper contrasts the results of demand estimates that do and do no not require explicit comparisons and-finds that each has a unique but complementary role in modeling demand.

INTRODUCTION

Understanding the determinants of demand for offerings with different benefits and prices is one of the more important planning functions of the marketing manager. Every time a new product is introduced or a current one modified, there is an implicit assumption about the effect of these changes on demand. A number of laboratory and field techniques exists for estimating demand for individual items before introduction into the marketplace (see Tauber 1977 for a review, and Sawyer, Worthing and Sendak 1979, and Nevin 1974, for examples).

Two techniques commonly used for estimating demand for a number of hypothetical product bundles are conjoint analysis (Green and Srinivasan 1978) and the dollarmetric comparison (Pessemier and Teach 1970). In both techniques consumers make evaluations on alternative competitive offerings. Conjoint analysis requires rankings or ratings of different profiles while the dollarmetric comparison asks for the difference in monetary value between pairs of offerings. Both tasks focus respondent attention on the relative value of objects defined by a set of product attributes.

Consider, however, the modeling of shopping contexts where such direct comparison of attributes do not occur; that is, situations where the consumer does not shop by comparing some or all of the alternatives but simply evaluates an alternative and on the basis of that evaluation makes a choice. In effect the consumer is deciding whether to buy or not rather than finding the best in a set. In such a choice mode, both dollarmetric and conjoint analyses are strictly inappropriate for predicting choice since the customer is not evaluating every product in a set, as these models assume, but merely deciding if a particular option is adequate. Consider as examples the home-buyer who purchases the first acceptable house, the industrial buyer who accepts the first bid that meets specifications, or the rushed shopper who selects the first gift in the correct price range. Olshavsky and Granbois (1979) review a large number of studies giving evidence of just such lack of explicit choice comparisons prior to purchase.

Retail credit insurance presents a similar situation. This insurance is offered to customers in connection with a retail credit purchase. It protects the customer's ability to make credit payments in the face of events beyond the debtor's control, such as death or the loss of earning power due to illness or layoffs. The insurance package is typically offered at a price which the customer may accept or reject but typically cannot modify. Furthermore, since credit insurance is a relatively small part of the entire transaction it is rare to switch stores on the basis of the credit insurance offering.

Thus, explicit comparisons are rarely possible in the purchase of credit insurance. Using this product class on an example, the purpose of this paper is to provide guidance to those firms whose customers generally make similar. Noncomparative, purchase decisions. Standard conjoint analysis, with a task that asks respondents to evaluate 16 credit insurance offers, is contrasted with a single choice task that asks for a simple "buy," "no buy" decision. It is shown that the single choice data can be analyzed quite efficiently using logistic regression and produces results that are consistent with theory and other research. For its part, the analysis of the 16 ratings results in a reasonable segmentation scheme that is difficult to derive using other methods. In addition some theoretical reasons are given for collecting and analyzing multiple ratings data even when this task is demonstrably different from the actual purchase situation.

THE CREDIT INSURANCE SURVEY

The survey was sent by mail to the customers of three retail firms that offer credit insurance. These three retail firms were chosen to be quite different in terms of (1) relative size, (2) breadth of line and (3) average income of customers, thereby assuring that various demographic and customer groups would be represented in the survey.

Conceptually, there were three parts to the questionnaire. The first described credit insurance and offered one plan in the context of a hypothetical retail purchase. This part attempted to stimulate the learning and simple choice that accompanies the sale of credit insurance on a retail transaction. The second part asked respondents to rate 16 insurance packages on a six-point scale of relative liking. This section is similar to commercial application of a standard conjoint task. Finally, the third section of the questionnaire asked a series of demographic and attitude questions to help categorize the results.

The purpose of the simulated purchase question was to estimate the effect of various changes in offerings or price on expressed willingness to purchase. The package offered varied over the coverages provided (life, accident and health, property, and employment) and four levels of price. Each coverage had associated with it a variable cost that contributed to the total cost of the package. The particular fixed cost level was then added to the costs of the coverages to derive the total cost of the package. Thus, packages with more coverages tended to cost mo e, making the set more realistic, but the effect of price was still estimable since the fixed cost varied across offerings.

Each respondent had an equal chance of evaluating one of the 64 (24 x 4) different packages. The administration of such a questionnaire was made feasible by having those parts that differed across respondents printed by a computer on pre-printed forms.

Following the decision on the individual package, the respondents were asked to rate 16 packages. These 16 formed an orthogonal array over the coverages offered and price so that for each respondent the main effect of each factor was estimable. Thus, for example, the overall effect of life insurance on liking could be evaluated for a respondent but not the interaction of life coverage and accident and health. Across respondents the particular orthogonal array was randomized so it was possible to estimate interactions for groups or segments.

Thus, the two parts of the credit questionnaire provide a chance to evaluate contrasting ways to model demand. The analysis and results of the simulated purchase question are presented followed by the results of the 16 ratings. These are shown to be quite different both in correct mode of analysis and in the managerial meaning of their results.

ANALYSIS OF THE SIMULATED PURCHASE QUESTION

For each of the 370 respondents who returned the questionnaire, the following data was generated: an indication that the respondent would buy (coded 1) or not buy (coded 0), the terms of the offer, and various customer characteristics. The objective of the analysis was to predict penetration, measured as the percent indicating "buy," as a function of the description of the offer and the customer.

A simple way to analyze this data is by a linear probability model which directly regresses the (0-1) choices against the predictors. This model is inappropriate and was not used for two reasons. First, the assumption of equality (homoscedasticity) of error variance is violated. This violation results in inefficient parameter estimates, in invalid confidence intervals and statistical tests (Nerlove and Press, 1973). Second, the linear probability model is logically inconsistent in that predicted probabilities may lie outside of the 0-1 range.

To avoid the problems inherent in a linear probability analysis, a logistic analysis was used. In this analysis, likelihood of purchase, instead of being a linear function of the predictors, is assumed to be related to them by a logistic or S-shaped function. Such a function is very similar to a family of sigmoid functions such as the normal ogive or the arcsin (Cox 1970). Thus logistic analysis is empirically indistinguishable from either probit analysis (Rao and Winter 1978), or angular analysis (Bock and Jones 1968). The critical properties of any of these analyses are that (1) the predicted probabilities are strictly bounded between 0.0 and 1.0, and (2) the marginal effect of any variable is greatest in the middle ranges and decreases as the predicted probabilities approach 0.0 or 1.0. Translated into marketing terms, this latter property implies that the effect of a variable on market share is lowest if the other aspects of the offer are very well liked (and thus leave few customers to win over), or are not liked at all (and thus put the offer outside of the consideration set). Thus both the logical consistency of the logistic model and its empirical assumptions are appropriate to many marketing situations.

The particular program used was a multivariate logistic program designed by Nerlove and Press (1973). This model assumes that there is a utility for each stimulus, (U ) that is a linear function of the levels of each of the predictor variables (Xij), so that

U_i = a_o + E_ja_jx_ij.   (1)

This utility is then related to the predicted penetration or quantity sold (Qi) by the logistic function,

Q_i = 1/(1+exp(-U_i))   (2)

so that

Q_i = 1/(1+exp(-a_o-E_ja_jx_ij).   (3)

The Nerlove and Press algorithm starts with the linear probability model and then searches for parameter values (ai's) that maximize the likelihood of the actual choices given their predicted probabilities. Significance tests for the parameters and the entire model are based on a chi-square test which is exact for large numbers of observations (Wilks 1972, p. 419).

EMPIRICAL RESULTS

The coefficients for the logistic regression predicting choice as a function of the offer are shown in Table 1.

TABLE 1

COEFFICIENTS OF LOGISTIC REGRESSION

The overall relationship was significant at the p<.05 level as were five out of the six coefficients. It is difficult to directly interpret these coefficients since they to not additively translate into probabilities but do so only through the logistic transform in Equation 3. Thus the advantage of the logistic formulation -- that the effect of a variable depends on the other variables that make up the package -- is a disadvantage in presenting the results to others.

In order to avoid these difficulties of interpretation, it is often useful, following Flath and Leonard (1979), to indicate changes in penetration given various reference stimuli. These estimates are shown in Table 2. The reference stimuli were chosen to span the range of options offered in the questionnaire. The item with the lowest predicted penetration (442) had only employment coverage and the largest price boost ($1.00). The items with the highest predicted penetration (74%) had all of the coverages and the lowest price boost (25%). Table 2 indicates that the coverages added between 10 and 20 percentage points to penetration, with greater gains (although the differences are not statistically significant) coming from accident and health and property coverages. Adding a dollar to the price of a package rather consistently dropped penetration by about 30 percentage points.

Another commonly used measure of price sensitivity is elasticity of demand, the percent change in penetration over the percent change in price. Given the logistic model, elasticity changes depending on the reference stimulus, but point elasticity can be easily computed for each. If Q is penetration and P is price, and B is the logistic coefficient for price, point elasticity can be derived from Equation 3 as:

e = (dQ/Q) + (dP/P)

e = (1-Q)P*B .   (4)

Using Equation 4 the elasticity of the average stimuli is -.71, so that a 10% increase in price results tn a 7% decrease in demand, and indication of rather substantial price sensitivity.

TABLE 2

PREDICTED CHANGES IN PENETRATION DUE TO DISCRETE CHANGES IN THE OFFER

EFFECT OF CUSTOMER CHARACTERISTICS ON PENETRATION

While Table 2 summarizes the sensitivity of customers to changes in the offering, it does not discriminate between different segments or customer groups. Customer characteristics may be used as interaction terms in the logistic regression to model changes in price sensitivity of various customer groups. First, however, the past research in the area is briefly considered. This foray is important to show the correspondence between this method and more traditional research.

Several studies provide some evidence as to the effect of customer characteristics on the price sensitivity of demand for credit insurance. Juster and Shay (1964) examined sensitivity to finance rates for "rationed" customers and "nonrationed" customers. A rationed customer was conceptualized as one who had difficulty securing as much credit as desired given regulated finance rates. Juster and Shay operationalized this concept as those with lower incomes who are in the early stage (first 15 years) of family development, and found that these rationed customers were indeed less sensitive than nonrationed customers to higher interest rates or monthly payments in hypothetical credit packages.

Similar results can be predicted for credit insurance for two reasons. First, to the extent that credit insurance lessens chance of foreclosure and thus increases the probability of obtaining future credit, credit insurance may be seen as a mechanism for increasing the supply of credit available for a rationed customer, and thus be differentially valued by that group. Second, in the context of a $400 retail purchase situation described in the questionnaire, the need for credit insurance to assure one's ability to pay such a relatively small level of indebtedness can be expected to come most strongly from those who do not have the economic slack to make payments in the face of an emergency. These are likely to be the same households who, on the credit supply side, are rationed. Thus, although the reasoning is different, the influences on the demand for credit insurance should parallel those for credit in genera

In an earlier study of attitudes towards credit insurance (Huber 1978), a stronger desire for credit insurance was indeed found among those with (1) less education, (2) lower income and (3) less optimism with respect to their current financial situation.

The data on individual credit insurance choices was used to test the effect of these customer characteristics on price sensitivity. New variables were formed by multiplying a dummy variable for each characteristic by the price of the offer. Thus the price coefficient was modified whenever that characteristic was present. Table 3 shows the change in the price coefficient due to home ownership, high income, and perceived financial security.

TABLE 3

THE EFFECT OF CUSTOMER CHARACTERISTICS ON PRICE SENSITIVITY

For example, the slope (dQ/dP) is significantly steeper for those with family incomes over $20,000 compared with those having less income. The three effects tested were statistically significant and in a direction expected by theory and past research. That is, high income, home ownership, and financial confidence were all expected to increase price sensitivity as manifested in an increase in the negative slope of the demand curve.

To summarize, a series of different individual choices across hypothetical products was efficiently analyzed using logistic regression. The model was generalized with the use of dummy variables to include customer characteristics. These characteristics had coefficients that were consistent with theory and past research. For many purposes it might be sufficient to stop the analysis at this point. However, it will be shown that an analysis of the relative ratings of the 16 plans provided additional insight into the nature of demand not tapped by the single choice question.

TRADE-OFF ANALYSIS OF 16 INSURANCE PROFILES

In the profile task respondents evaluated 16 insurance packages. The analysis of this data was identical to the logistic analysis of the single choice data except it was done at the level of the individual rather than the group and the dependent variable was the rating rather than the choice. This last difference enabled the use of standard rather than logistic regression. The average values for the individual coefficients are given in Table 4. The meaning of each coverage coefficient is the expected change in rating if that coverage is added at no charge. For example, life insurance adds on expected 1.23 units out of 6.0 possible to the average respondent's rating. Increasing the price of the package decreases the rating in proportion to the price coefficient so that if life insurance were offered at a $1.00 incremental charge its expected rating would increase by 1.23 less 1.09 for the cost = 0.14 units.

TABLE 4

THE AVERAGE RAW COEFFICIENTS AND INDIFFERENCE VALUES FOR THE COMPONENTS OF THE OFFER

The dollar value of each coverage was estimated by dividing the coefficient of money by the coefficient for coverage. This trade-off value has the advantage of being independent of the six-point concept scale and represents the price at which the value of the coverage is just offset by its incremental cost. These indifference values are given in the third line of Table 4. For comparative purposes the analogous indifference prices from the logistic analysis of the single choices are given on the fourth line. These provide the price at which predicted penetration remained unchanged while the line above indicates the price at which the predicted rating was unchanged. Comparing these lines the rating indifference prices are different from the penetration indifferences in two ways. First, the dollar value of all coverages is greater in the multiple task. Second, there is more discrimination between coverages in the rating task, both in terms of the estimated differences between coverages and the standard errors of those estimates (comparing the standard errors in Table 1 and Table 4).

Thus it appears that there are differences in the results from the analyses of the two kinds of data. While the reasons for and implications of such differences are discussed later, an even greater contrast may be found in a segmentation analysis whereby individual indifference prices of the coverages are broken down by demographic subgroups.

Table 5 illustrates the individual trade-off values broken down by demographic subgroups. It is possible to characterize those groups that expressed the largest trade-off values for the various kinds of insurance. Since the managerial question often centers around the kinds of insurance to offer customers, such analysis is useful in defining optimum packages to different customer segments.

TABLE 5

THE EFFECT OF CUSTOMER CHARACTERISTICS ON THE TRADE-OFF VALUES OF INSURANCE TYPES

The highest trade-off value for life coverage came from those who had less than a high school education, were married, and had three or more residents in an owner occupied dwelling. Thus, the ideal market for credit life appears to be the family and the promotional emphasis would be on the continued well-being of the family members.

By contrast, the other three forms of credit insurance: accident and healths property and employment, all had the highest trade-off values among those who had more education, were under 35 years of ageS unmarried or had small families, and rented rather than owned their dwelling. These characteristics reflect customers who may be more concerned with perpetuating their own life style rather than assuring family continuity. Accordingly the coverages might best be promoted by stressing the use of the product that is being purchased and the positive benefits of credit insurance allowing the preservation of one's life style in the face of various eventualities.

As plausible as the above segments may be, they had not been revealed in previous research. An earlier study had directly asked for attitudes toward four kinds of credit insurance coverages (Huber 1978, p.11) and had not found theses differences in orientation. Similarly in the logistic analysis of individual choices the interaction of customer characteristics and the different kinds of credit insurance were in the same direction as the trade-off study but failed to reach required levels of significance.

Thus, the analysis of the 16 trade-off ratings produced the expected greater sensitivity to customer characteristics by suggesting a segmentation strategy not revealed elsewhere.

SUMMARY: A CHOICE-OF-ONE VERSUS MULTIPLE RATINGS

Using the credit insurance data as an example, the preceding has compared the use of a single choice task with one that requires a relative evaluation of many alternatives. It was shown that the results from these two tasks differed in several ways. First, the indifference prices from the two methods would lead to somewhat, although not markedly different conclusions. For example, the single choice data put property coverage first while the multiple ratings put life first. Second, the multiple ratings resulted in far more stable parameter estimates. This stability follows from the fact that ratings increase the sample size by a factor of 16 and because there is more information in a 6-point scale than there is in binary choice. This additional power allows the kinds of segmentation analyses that can only be suggested by other methods.

In spite of its statistical power, the theoretical and conceptual differences between multiple ratings and single choice tasks argue against these being substitute methodologies. Indeed, consider the logical link between the two. An individual could consistently accept an item that is least liked in a rating task, simply because all of the items are acceptable taken individually, Conversely a person could reject what he or she considered to be the best item in the set because no insurance was needed by that person. Put differently, the relative ratings only compare items, they do not indicate the general acceptance level of the set. Thus there is only a weak correspondence between an individual's ratings and his or her choice.

Worse still, the fact of making comparisons may alter the criteria for making decision. Such ratings may share with paired comparisons (see Blankenship 1966) a tendency to highlight product differences that may not be as important in a monadic, or single choice context. Indeed, the greater sensitivity to the different coverages found in the analysis of the rating data is consistent with just such a task effect.

Thus, if a firm has a product whose purchase conditions parallel credit insurance in the sense of single choices that can be either accepted or rejected, then the fore-going would argue that demand be modeled by single choices rather than multiple ratings. That is, if a conflict developed between the methods, the single choice method should dominate because its task best simulates the actual purchase condition. However, the methods need not conflict and may be seen as complementary. Indeed, there are three reasons for firm to collect the multiple ratings data even if it does not precisely simulate their customers' purchase behavior.

First a firm may wish to collect multiple ratings as a biased but more reliable estimate of the single choice sales context. The higher reliability allows more options to be considered and permits the evaluation of elaborate segmentation strategies. The most promising of the options or segments can then be tested using the single choice task. Such a perspective on multiple ratings as a prior screening parallels Day's (1968) suggestion that multiple comparisons be used in the early stages of product design to develop a small set of good candidates for the less powerful but more valid monadic tests.

Secondly, a firm may collect multiple ratings that may be paradoxically more valid in the long term than the single choice task. This possibility stems from the fact that in a multiple rating task respondents become familiar with product differences. This learning may parallel the development of the choice criteria (Howard 1977) that evolves as consumers develop experience with the product class. If such a process occurs then the values derived from the multiple ratings may foreshadow single choices as the product class becomes more mature. For example, in the credit insurance data, the single choice task revealed less difference between the coverages than did the multiple ratings. A company relying on single choice data might be vulnerable to a promotional campaign by a competitor that stresses differences between coverages.

Finally, a firm may use results from multiple ratings data simply as the best mechanism for maximizing consumer welfare. That is, even though choices in the marketplace may not be made with full knowledge of alternatives, certainly a utility surface generated with such consumer knowledge is superior from the consumer's perspective to one that limits possible information. Thus, it can be argued that consumer well-being will be improved by using the results from the ratings data over the single choices, and that a firm is better off knowing these results even if they are not used because of pressure to maintain short run sales and profitability.

To summarize, this paper has been made a distinction between two kinds of purchase situations. The first involves a decision made with fairly good knowledge of the alternatives where a choice is made from among competitive offerings. The second involves a choice to buy or not buy a particular item without explicit product comparisons. While most decisions lie between these two extremes, the multiple ratings task appears to simulate the first context while the second context is best simulated by the single choice task.

From the example given, it appears that even if a firm has an offering where the decision is a single choice mode (as credit insurance clearly is) both methods of data should be collected. The logistic analysis provides a reasonable estimate of the effect of the offering and price on short term demand while the multiple ratings result in stable, segment-based information that may be the best predictor of long term demand. Thus both methods have conceptually separate but complementary uses in modeling demand.

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