Measuring Consumer Retail Store Loyalty

ABSTRACT - One major problem in retail management is predicting the number of customers visiting the store in a given time period. This number is of course in the short term influenced by several marketing variables, some of which are under the store's control (price deals, promotion, advertising) and some that are beyond the decision maker's control (week- day, time of day, time of month). More important than short term variation in the number of customers, however, is the structural shopping behavior developed during long term factors such as store location, assortment policy, general price level, parking facilities, etc.



Citation:

Ole Stenvinkel Nilsson and Jorgen Kai Olsen (1995) ,"Measuring Consumer Retail Store Loyalty", in E - European Advances in Consumer Research Volume 2, eds. Flemming Hansen, Provo, UT : Association for Consumer Research, Pages: 289-297.

European Advances in Consumer Research Volume 2, 1995      Pages 289-297

MEASURING CONSUMER RETAIL STORE LOYALTY

Ole Stenvinkel Nilsson, Copenhagen Business School

Jorgen Kai Olsen, Copenhagen Business School

ABSTRACT -

One major problem in retail management is predicting the number of customers visiting the store in a given time period. This number is of course in the short term influenced by several marketing variables, some of which are under the store's control (price deals, promotion, advertising) and some that are beyond the decision maker's control (week- day, time of day, time of month). More important than short term variation in the number of customers, however, is the structural shopping behavior developed during long term factors such as store location, assortment policy, general price level, parking facilities, etc.

In order to be able to quantify the effect of such factors, measures that reflect structural shopping habits are needed. Also, the increasing interest in creating customer loyalty towards retail stores by direct marketing activities like customer clubs, and member card identification stresses the interest in loyalty measurement.

In media planning, great attention has long been paid to such topics since readership loyalty is a key factor in determining the effect of a given media plan in terms of the number of persons (within a specified target group) exposed once, twice, and so on. The exposure frequency distribution is the central planning tool. From this concept several simpler performance measures have been derived. Examples are: Reach-the percentage of the target group exposed at least once, Frequency (FREQ)-the average number of exposures among those exposed at least once, Gross Rating Points (GRP)-the expected total number of exposures, Effective Reach (ERP)-the number of exposures within a certain range.

In brand management still other loyalty measures have been suggested. Examples are: Market share, brand choice distribution, number of consecutive times a brand is bought, volume of brand bought, and a brand's volume share of category.

In this paper we formulate a general model that is able to describe the loyalty structure in a given market. From this model we derive a set of key measurement tools describing retail store loyalty. The concepts are inspired both by media planning and brand management but since the model behind the concepts is a general one, the concepts may be seen as a general tool to describe many different kinds of loyalty, for instance readership loyalty, brand loyalty, loyalty towards ways of transportation, and, in particular, store loyalty. The loyalty concepts have some obvious analytic advantages, they are easy to measure, and together they give a parsimonious description of (store) loyalty.

The data needed for estimating the concepts are standard aggregate measures available to both brand managers and chain store distributors. The estimation is based on realistic behavior models of consumer store choice and uses a technique familiar to latent class modelling.

1. THE LOYALTY CONCEPT

In this paper we refer to the loyalty concept as a choice pattern observed during some time, indicating that the consumer has some degree of preference for a given subject, in this case the store.

Before modelling shopping behavior it is important to understand that store choice behavior and hence loyalty to a store is a complicated phenomenon. Buying decisions consist of several subdecisions: Decisions on 1) total number of shopping occations per time period, 2) amount of money spent on each occation, 3) choice of outlet on each occasion. These decisions are not only interrelated, but furthermore they depend on demographic and other background variables. In particular, the type of shopping occation plays a central role. According to Engstrom and Ursen (1987) the store choice depends on the shopping situation (daily shopping, weekend shopping, shopping for guests, etc.). Hence, ideally loyalty should be defined and measured in relation to the specific shopping situation, the number of shopping occations, and for homogeneous consumer segments. However, due to model parsimony and lack of detailed data some assumptions have to be made.

Another point in identifying central figures of loyalty, is the fact that loyalty may be measured both in relation to number and share of visits to the store and to amount and share spent in the store. We will now consider various performance measures for a store. All measures refer to a certain time period, in this analysis we have chosen a month. Since performance may be measured in two dimensions, in terms of shoppingvisits or in terms of revenue, both separate sets of measures will be suggested:

Shopping visits:

Total number of visits

Total number of customers

Distribution of visits by customers

Average visits per customer

Share of customers ever visiting the store

Share of customers visiting the store at least b times

(b being a figure chosen by the analyst)

Store's share of a customer's total number of visits.

Shopping revenue:

Total revenue

Distribution of revenue by visits

Distribution of revenue by customers

Average revenue per visit

Average revenue per customer

Store's share of a customer's total amount bought.

While data concerning visits is collected externally by research institutes on a regular basis, revenue data is only available internally in the store. Since our data comes from external sources (frequency information for a cross-section of large outlet chains) this paper concentrates on measuring loyalty by looking at visiting patterns, even though we recognize that this analysis is only part of the story. (For instance, is a consumer that spends 90 % of his monthly amount of buying in store A, but only visits store A 10 % of his total visits more or less loyal than a consumer that buys 10 % of the amount by visiting the store 90% of the times?).

There exist some fundamental relationships between several of these store performance measures. These relationships will be presented in section 4, and it is demonstrated that most of the concepts are easily derived from the marginal and conditional visiting frequency distribution. These distributions are often determined empirically based on a sample survey. In this paper we propose some possible formula-based distributions of one single outlet. It is demonstrated how a convolution of three Poisson distributions is able to fit some of the empirical distributions met in practice.

2. FUNDAMENTAL MODEL STRUCTURE

In this section we formulate a general model for describing loyalty within any area. The model has earlier been demonstrated to describe readership data (see Nilsson and Olsen (1992)), and brand choice data (see Olsen (1994)). The aim of this paper is to reformulate the model according to the present problem and apply the model on aggregate outlet choice data.

It is important to point out that the model presented here does not deal with those elements of loyalty that are connected to short-term behavior described in terms of number of consecutive times a certain act is performed (inertia, reinforcement, variety seeking, etc.). Our model focuses on and tries to describe the long-term behavior structure that may be found in any kind of human activity concerned with repetetive choices among a given set of alternatives.

The fundamental concept to describe any kind of choice behavior of the individual is the simultaneous distribution of the number of times each alternative is chosen. In the present case, the individual's simultaneous distribution of the number of visits during a month among different stores is fundamental. From this, it is possible to derive any other distribution that might be of interest. Thus, by making appropriate aggregation and conditioning it is possible to calculate

1 the individual's marginal distribution of visits

2 the market's marginal distribution of visits

3 the individual's marginal distribution of visits to a given store

4 the market's marginal distribution of visits to a given store

5 the individual's conditional distribution of visits to the store, given a total number of visits

6 the market's conditional distribution of visits to the store, given a total number of visits

From these distributions several loyalty concepts can easily be derived, as will be shown in sections 3 and 4.

However, since it is impossible to formulate different models for each individual and unrealistic to assume identical behaviors of all individuals, we propose a segmented model that assumes identical behavior within each segment. The segmentation is very flexible. It can be defined by demography, attitudes and lifestyles, or, which will be demonstrated later in the paper, by usage rate, i.e. in this case the number of shopping occations per month.

The way we handle heterogenity is somewhat different to what is common in the litterature. Often a model of individual behavior is established and heterogenity is introduced by assuming that the model parameter(s) are distributed according to some population distribution. Well-known examples of such mixing distributions are the Binomial-Beta distribution, the Poisson-Gamma distribution and the Multinomial-Dirichlet distribution. We do not choose this tradition for three reasons. Firstly, the resulting market distribution (for instance the Poisson-Gamma distribution results in a Negative Binomial Distribution, NBD) is not always flexible enough to give an adequate description of empirical distributions found in practice, simply because it is unimodal, which may not be empirically true. If for instance, a store in order to increase loyalty has started a customer club, the segment of club members will almost certainly have a distribution concentrated to the right, while non-members may have a distribution concentrated to the left, resulting in a bi-modal market distribution. In addition, the "mixture" distribution Gamma or Beta do not contain any explanatory power at all. A segmentation made by the analyst is far more able to explain differences in behavior (take the customer club as an example). Secondly, practitioners using the model have much harder to understand the above models than a model which is in fact just a weighted average of a much simpler structure. And thirdly, the mixing distribution taking account of heterogenity is often chosen mainly in order to produce "nice" results and not because of realism.

The model has the following characteristics:

It is a stochastic model of individual behavior, i.e. the model is formulated at individual level, which provides much greater realism and flexibility than aggregate models.

The model assumes segment-wise identical and independent behavior, i.e. it is established for an operational number of segments.

If data on individual level is available, estimation of the model parameters is straightforward. However, the model parameters may also be estimated on aggregate market data, which are not segmented in advance. In fact, the trick is to estimate the behavior parameters of each segment and relative segment sizes simultaneously, based on aggregate data.

We now introduce some notation:

Let

Ni := Number of times a random consumer within the i'th segment makes shopping visits during a given time period (a month)

Ni ~ Poisson (li)

f(n i) = EQUATION (1)

(1) is the individual's marginal distribution of visits. To establish the market's marginal distribution of visits we just have to make a weighted average of (1), using the relative segment sizes as weights. If there are s segments and the relative segment size is qi, it follows that

EQUATION (2)

(2) is not a Poisson distribution, but a weighted average of Poisson distributions and may take any possible form, depending on the parameters li and the size of the qi's. Thus the model is very flexible and able to fit many types of empirical distributions.

We now consider m different outlets. It is assumed that all segments have access to the same set of stores. However, this assumption may easily be relaxed by setting some of the choice probabilities to zero. Then

Xi := [(Xl,X2,...,Xm)|ni]

is a conditional random vector indicating the individual's number of visits at each of the m outlets, given a total of ni visits.

Under the assumptions that consumers on the i=th segment have identical, constant and independent choice behavior it can be shown that the individual's simultaneous distribution of visits tothe m stores, conditional to the total number of visits, (Xi|ni) follows a Multinomial distribution with parameters (mi) and (pi1,Pi2,...,pim). In this distribution the number of visits to a given store is dependent of the number of visits to other stores (due to the fixed total of visits).

The model structure is flexible enough to account for any kind of heterogenity. Thus some of the li's may be equal, while the pij's are different, or the ki's may be different, while some of the pij's are equal, or both parameters may vary from segment to segment.

The individual's simultaneous distribution of 1) the total number of visits and 2) the number of visits to each of the m stores, f(ni,xi), is therefore the product of the marginal visiting distribution (1) and the conditional multinomial store choice distribution

EQUATION (3)

From (3) one can derive the individual's simultaneous (unconditional) distribution of Xi=(Xi1,Xi2,...,Xim), the number of times a random consumer from segment i visits each of the stores. After some calculation and reduction it can be shown that the simultaneous unconditional distribution of the number of visits to each of the stores is given by a product of Poisson distributions with parameters lipij

EQUATION (4)

It is seen directly from (4) that the marginal distribution of the j'th store is also Poisson distributed with parameter lipij, i=1,2,...,s and j=1,2,...,m.

Xij~ Poisson(lipij)

The marginal distribution of the j'th store can also be established in another way by starting with the individual's conditional distribution of visits to outlet j. When the simultaneous distribution of all stores is multinomial, the distribution for store j is known to be binomial

EQUATION (5)

The individual's simultaneous distribution of (ni,xij), i.e. the total number of visits and the number of visits to store j, is therefore the product of the marginal visiting distribution (1) and the conditional binomial store choice distribution (5)

EQUATION (6)

From (6) the marginal (unconditional) distribution of the number of times a random consumer from segment i visits store j is given by summation

EQUATION (7)

It is easily shown that the resulting distribution of the number of visits to store j is in fact the same as found earlier, i.e. Xij -Poisson(lipij).

This nice result is easy to understand and interpretate, since it states that the expected number of times a consumer in segment i visits a given store during a time period (a month) is equal to the expected number of shopping occations times the probability of choosing the given store at a given occation. What is not obvious in advance, however, is the fact that both the simultaneous and the marginal visiting distributions are Poisson. In particular, this implies that the number of times a consumer visits store j is independent of the number of times he visits store k during a given time interval. Dependency only occurs when the total number of visits is fixed, i.e. in the conditional distributions.

From (7) the market's marginal distribution of Xj, the number of times a given store is visited during a period, is easily derived simply by making a weighted average of the distributions of each segment. With relative segment size qi, it follows that

EQUATION (8)

(8) is not a Poisson distribution, but a weighted average of Poisson distributions and may take any possible form, depending on the parameters lipij and the size of the qi's. Thus the model is very flexible and able to fit many types of empirical distributions.

From the individual's marginal distribution (7)and the market's marginal distribution (8) the conditional distributions of the individual and the market, called fc(xij) and fc(xj) respectively, are (4) easily calculated. The conditional distributions provide the number of visits to a certain store, given that the consumer has visited the store at least once a month. This is derived simply by dividing (7) and (8) by (14(0)). The marginal and conditional market distributions play a central role in measuring the aggegate loyalty structure as seen in section 5. And the marginal and conditional individual distributions are the basis of measuring individual loyalty as demonstrated in section 4.

4. INDIVIDUAL LOYALTY MEASUREMENT

In this section we present some measures of loyalty that may be used to characterize the individual. Since our model assumes segment wise identical behavior, the measures express segment loyalty as well. The measures are derived directly from segment i's visiting distribution (1) and the visiting distribution to store j (7). The measures provide detailed information on the loyalty of the individual that may be analyzed further in order to establish customer and store profiles. Further analysis on how different marketing efforts affect each of the loyalty measures gives valuable insight into individual choice behavior. The measures describing the behavior of an individual from segment i include the following:

1. Total visiting intensity

2. The store's visiting intensity

3. The store's share of the total number of visits (market share)

4. The share of customers ever visiting the store (customer share)

5. The share of customers that are loyal to the store (loyalty share)

6. The store's conditional visiting intensity

While (1) - (4) do not explicitely express loyalty in the normal sense of the word, they are interesting since they often correlate closely to (5), the traditional loyalty figure. And they are much easier to measure, giving rough indications of loyalty. In fact, a main point of our study is to investigate whether this correlation holds true for all types of stores. (6) is a measure of usage rate, given that the customer belongs to a certain loyalty class. This measure is explained in detail below.

Since both (1) and (7) are Poisson distributions, the key figures are particularly simple. Thus

        E(ni)     =      lipij      (9)

with  V(ni)    =     li         (10)

and   E(Xij)   =    lipij     (11)

with  V(Xij)   =    lipij     (12)

By dividing (11) by (9) we get the market share of store j in segment i simply as the choice probability

Mij = pij  (13)

The customer share of segment i is calculated as 1 - fj(0) in(7). The customer share is the share of segment i that ever visits store j, i.e. the same concept as reach in media planning.

The individual/segment loyalty share of the store is defined as the share of customers in segment i visiting the store at least b times during a time period, b being a number chosen by the analyst (that may be varied according to the purpose of the study and the value of lj). The loyalty share is calculated as an upper tail probability of fj(xj)

EQUATION  (14)

Of course Lij(b) is a decreasing function of b. By comparing loyalty shares for different segments a profound understanding of the loyalty structure and profile of the store is obtained.

Finally, the store's conditional visiting intensity is a new concept that expresses the consumer's average number of visits to the store, given that he visits the store at least b times. The measure is calculated as the expected value of the marginal visiting distribution of store j, truncated from b and up, and divided by the loyalty share (14). The concept that is a generalization of the concept of frequency, well-known in media planning (setting b = 1) provides information on the usage rate of customers belonging to a certain loyalty class and is therefore central in assessing the customer value of different loyalty classes.

5. MARKET LOYALTY MEASUREMENT

In this section we present some aggregate measures of loyalty that are simply derived from the market visiting distribution (2) and the marginal visiting distribution at store j (8). The same measures of loyalty that exist on individual/segment level can of course be established on aggregate market level. This allows for a more parsimoneous description than the individual analysis which may be relevant in situations where a great number of outlets are compared. An example of this is presented in section 7, where we compare results from 10 major retail chains. As on individual level the measures include

1. Total visiting intensity

2. The store's visiting intensity

3. The store's share of the total number of visits (market share)

4. The share of customers ever visiting the store (customer share)

5. The share of customers that are loyal to the store (loyalty share)

6. The store's conditional visiting intensity

From the market's marginal visiting distribution (2) the expected number of shopping visits (visiting intensity) per month is given by

EQUATION (15)

with variance

EQUATION (16)

Similarly, from (8) the number of visits to the j'th store has the following expected number and variance

EQUATION (17)

and

EQUATION (18)

By dividing (11) by (9) the j'th store's market share is given by

EQUATION (19)

which is not the same as Sqipij, the weighted sum of store choice probabilities of each segment since the number of visits may vary from segment to segment.

The customer share of the store is simply calculated from (8) as 1-fM(0). The figure indicates the share of all customers that ever visits the store and may be seen as the share that has not completely rejected the store. The comparison to the concept of media reach holds true also at the aggregate level.

The loyalty share of the store is defined as the share of customers visiting the store at least b times during a time period. On aggregate level the loyalty share is calculated from fM(xj)

EQUATION (20)

If presented graphically Lj(b) is a simple concept that may be used to compare the aggregate loyalty structure of different stores. Examples for 10 major Danish store chains are presented below.

Finally, the conditional visiting intensity of the store is defined in a way similar to the individual level, and calculated from the market distribution (8).

This concludes our general model development. In section 6 we present a spreadsheet program based on the general model. The software is developed as decision support to describe and analyze store loyalty. This model assumes that the model parameters have already been estimated. In section 7 we address the estimation procedure. Based on empirical data we present a special case of the model and illustrate how a least squares procedure may be used to estimate and calculate the key concepts of loyalty developed in section 4 and 5.

6. A DECISION SUPPORT MODEL OF STORE LOYALTY

In this section we present a spreadsheet model that has been developed to facilitate calculations of the model and make presentations of the loyalty concepts simple to use in practice. The general model operates with s segments and m different stores. The present version of the software has been developed for 5 segments and 3 different stores. Input to the model is presented in Figure 1. As seen from the figure, all that is needed is estimates of the parameters li indicating the expected number of shopping visits of each segment, and the choice probabilities with which a customer in segment i chooses store j, pij. Finally, estimates of the relative segment sizes are also needed. We address the estimation of the parameters in the next section.

FIGURE 1

THE CUSTOMER'S STORE CHOICE. INPUT DATA

As seen from the example data store C is the preferred store by all 5 segments but in varying degree. Most of the heavy users prefer C, while A has its greatest preference among customers with infrequent shopping patterns.

From this input the program calculates the following figures for each segment and the entire market:

1. The distribution of the total number of visits

2. The distribution of visits to each of the stores

3. The conditional distribution of visits to each of the stores, given that the store is ever visited

Besides, the key concepts of loyalty presented in section 4 and 5 are calculated both at segment and market level

1. Total visiting intensity

2. The store's visiting intensity

3. The store's share of the total number of visits (market share)

4. ne share of customers ever visiting the store (customer share)

5. The share of customers that are completely loyal to the store (loyalty share)

6. A graphical presentation of the loyalty share as a function of b

The key concepts are calculated both from the marginal and from the conditional distribution. The marginal figures characterize the entire market, while the conditional figures characterize only that part of the market that ever visits the store. In Figure 2 the market distributions of each of the 3 stores are presented. These distributions are the basis on which the key concepts are calculated. As an example, store C's loyalty concepts of each segment are presented in Figure 3. In Figure 4 the market loyalty figures of the 3 stores are compared.

All stores have visiting distributions that are skewed to the right. And because store A has its main preference among low frequent buyers its distribution is by far the most concentrated on small number of visits. Store C has a distribution that, although also skewed to the right, is much more "normal". The distributions of Figure 2 are all mixtures of 5 Poisson distributions with intensities lipij and weights qi.

Interesting differences between the segments are observed from Figure 3. Thus while the low frequency segment I has the least probability of visiting the store at all during the time period considered, segment I has the largest share of complete loyalty. In contrast, the high frequency segment 5 has a zero share of complete loyalty to store C. But nevertheless the number of visits to C from a consumer in segment 5 is far greater than in the other segments.

For all 3 stores the market loyalty share is very low. This is because we calculate complete loyalty (meaning that on all shopping occations store j is chosen). If a less restrictive loyalty concept is used the figures would of course be different. This is illustrated in Figure 5 that shows the loyalty share as a function of the value of b in (20). It is seen that for all values of b store C dominates store B, which again dominates store A.

7. ESTIMATING THE SEGMENTED VISITING DISTRIBUTION

The simultaneous visiting distribution presented in section 3 is quite general. In principle it is possible to estimate a model of s segments and visiting intensities and choice probabilities of each segment, if an empirical simultaneous distribution of visiting frequencies were available. Since our empirical distributions are marginal for one single store (store j) we are notable to demonstrate how the generel model is estimated. Instead we consider a special case of the model using only data from one store at a time. Furthermore, we assume that the market consists of only 3 segments: One segment that almost never visits the store (has rejected the store), a segment that sometimes visits the store (is indifferent to the store) and a segment that uses the store very often (is loyal to the store). We use an empirical aggregated distribution to estimate 1) the visiting intensities lipij of each segment and 2) the relative segment sizes qi. An estimation program finding the lipij - and q-values by minimizing the squared differences between the observed and the theoretical distribution has been developed, and some results are presented in this section.

The estimation program was first developed to estimate a model where the behavior was modelled as a binomial distribution and not a Poisson. This model aimed at describing readership loyalty and the estimation was done on 10 empirical frequency distributions of Danish weekly magazines from the Danish Media Index. In this case it was necessary to put a priori bounds on some of the parameters in order to keep them separated. This was not necessary in the present case. The procedure presented here is based on unrestricted least squares. Figure 6 presents estimation results for the 10 greatest retail chains in Denmark. The data used in the estimation is aggregated visiting frequency information collected as part of the media index. Data may be broken down by sex, age and other demographic variables. An analysis of these segments is presented in Figure 7.

FIGURE 2

VISITING DISTRIBUTIONS OF STORE A, B, AND C

FIGURE 3

SEGMENT LOYALTY CONCEPTS OF STORE C

FIGURE 4

MARKET LOYALTY CONCEPTS FOR STORE A, B, AND C

Looking at the parameter estimates it is a general pattern in all 10 stores that one lipij is taking a rather low, another is taking a rather high value, while the third value is in between. However, there are interesting differences in the actual values from one store to the other. Also, the segment sizes show a pattern that is similar for all stores. The greatest part of the customers have rejected the store, a somewhat smaller group are indifferent to the store and only a small share has preference to the store. But also the q's are varying a great deal from one store to the other, giving interesting information on relative attractiveness of different stores.

In Figure 7 some of the aggregate data are broken down by sex and age. We analyze two of the chains along these lines, Super Brugsen and Irma. While Super Brugsen is by far the largest Danish chain with around 13% of the total sales area of the sector and, one might add, without any special profile, Irma is one of the smaller chains with about 2% of the sector sales area, but with a fairly clear quality profile. The estimation gave the following result (Figure 7).

While Super Brugsen does not show any significant parameter differences neither across sex nor age, Irma seems to have its most loyal segment among older people, especially women, while young persons have low visiting intensities in Irma.

FIGURE 5

GENERALIZED LOYALTY SHARE

FIGURE 6

ESTIMATES OF VISITING FREQUENCY PARAMETERS OF 10 DANISH RETAIL CHAINS

FIGURE 7

SEX AND AGE SHOPPING PROFILE OF SUPER BRUGSEN AND IRMA

8. DISCUSSION

In this paper we have developed a general stochastic model of consumer choice behavior that may be used as a framework for analyzing consumer loyalty. The model is applied to store choice behavior, but may describe other kinds of choices as well. In fact we have used the same structure (in a modified form) to analyze media habits and brand choice behavior. The central concept of the model is the consumer's simultaneous distribution of the number of times each alternative is chosen during a certain time period. From this individual distribution a set of individual loyalty measures have been derived. Together the key concepts characterize the loyalty structure of the market and provide information that is easily calculated from standard marketing research data.

When calculated on individual level the loyalty measures may be used for customer value segmentation, an important addition to demographic and psychographic segmentation. On aggregate level the measures characterize the profile of different stores. An example for 10 major Danish retail chains is presented.

It is important to notice that in this paper we only use the word loyalty for observable behavior patterns. The cognitive aspect Of loyalty, i.e. a positive attitude towards a certain alternative, is not included in the present model. This is quite deliberate since we are dealing with long-term loyalty structure more than short term variations in behavior. A positive attitude that is not expressed in action during some time is of limited interest to the store. On the other hand, the customer satisfaction with the alternative chosen most often should not be neglected since this factor is a key determinant of the competitive strength of the store.

REFERENCES

Colombo, R.A. and D.E. Morrison (1989) " A Brand Switching Model with Implications for Marketing Strategies", Marketing Science.

Ehrenberg, A.S.C. (1988), Repeat Buying: Facts, Theory and Data, Oxford University Press.

Engstrom Hans and Hanne Hartvig Larsen (1987), Hush oldn ingernes Butiksvalg-Indkobsadfard for dagligvarer (in Danish), Copenhagen.

Jeuland, Abel P., Frank Bass and Gordon Wright (1980), A Mullibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes, Operations Research.

Lilien, G.L., Ph. Kotler and K.S. Moorthy (1992), Marketing Models, Prentice-Hall, Englewood Cliffs, N.J.

Nilsson, Ole Stenvinkel and Jorgen Kai Olsen (1992), "Exposure Frequency Distributions and Related Topics", Working Paper, Marketing Institute, Copenhagen Business School.

Olsen, Jorgen Kai (1994), "Maerkevalgfordelingen pa et segmenteret marked" (in Danish), Research Paper, Marketing Institute, Copenhagen Business School.

----------------------------------------

Authors

Ole Stenvinkel Nilsson, Copenhagen Business School
Jorgen Kai Olsen, Copenhagen Business School



Volume

E - European Advances in Consumer Research Volume 2 | 1995



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