Patronage Behavior Toward Shopping Areas: a Proposed Model Based on Huff's Model of Retail Gravitation

ABSTRACT - Among various gravitational models, Huff's probabilistic model of retail gravitation is probably the most widely used model. Its ability as an explanatory tool, however, is handicapped by the fact that it includes all potential shopping areas in its competitive system. This paper proposes a new model based on the concept of choice set. Results from a large scale study in a Canadian city indicate that the proposed model substantially outperforms Huff's model, and can be used for both predictive and explanatory purposes.


Chow Hou Wee and Michael R. Pearce (1985) ,"Patronage Behavior Toward Shopping Areas: a Proposed Model Based on Huff's Model of Retail Gravitation", in NA - Advances in Consumer Research Volume 12, eds. Elizabeth C. Hirschman and Moris B. Holbrook, Provo, UT : Association for Consumer Research, Pages: 592-597.

Advances in Consumer Research Volume 12, 1985      Pages 592-597


Chow Hou Wee, National University of Singapore, Singapore

Michael R. Pearce, The University of Western Ontario, Canada


Among various gravitational models, Huff's probabilistic model of retail gravitation is probably the most widely used model. Its ability as an explanatory tool, however, is handicapped by the fact that it includes all potential shopping areas in its competitive system. This paper proposes a new model based on the concept of choice set. Results from a large scale study in a Canadian city indicate that the proposed model substantially outperforms Huff's model, and can be used for both predictive and explanatory purposes.


Since the emergence of shopping centers in the 1950's and 1960's, retail sales have been shifting increasingly toward such centers. Estimates indicate that shopping centers will account for 50, of all retail sales by 1990 (Dickinson 1981, p.57). In a recent study (Prestwick 1980), 47% of the sampled shoppers in a major shopping mall reported that they were there because of the mall itself. Thus, almost half of the shoppers did not make their shopping locational choice because of the attraction of specific stores or products and services, but instead were attracted by some aspects of the mall and its complex of units. Related to the development of shopping centers is the conscious attempts by many downtown retail areas to get organized as "business entities" to react to the increasingly threats posed by shopping centers (Spalding 1981; Petto 1983).

The evolution of planned and organized shopping areas such as shopping centers and revitalized downtown areas has several implications. To the consumer, the evolution represents another level of patronage decision in the form of increased choices between different shopping areas. To the marketer, it means an increasing need to attract the consumer to the shopping area, and not just to a particular store. The importance of promoting the whole shopping area thus takes on more significance than promoting a particular store. Related to this, therefore, is the need to understand the main factors that affect the choice of shopping areas by consumers, and how they can be attracted.


There is no doubt that organized shopping areas will take on increasing significance in the decision-making process of consumers in the future. Unfortunately, there have not been much research in understanding consumer patronage behavior toward shopping areas. Within the retailing area, the gravitational type of models have been traditionally used by researchers and retail managers to predict retail trade areas and consumer patronage patterns (Bucklin 1971a and b; Converse 1949; Huff 1962). Among the various gravitational models, Huff's probabilistic model of retail gravitation is probably the most well-known and used (Huff 1962, 1963, 1964, 1981). The mathematical formulation of Huff's model is expressed as follows:



Pij = the probability of a consumer at a given point of J origin i travelling to a given shopping center j;

Sj = the square footage of selling space devoted to the sale of a particular class of goods by shopping center j;

Tij = the travel time or distance or costs involved in getting from a consumer's travel base to shopping center j; and

l = a parameter which is to be estimated empirically to reflect the effect of travel time or distance on various kinds of shopping trips.

In essence, the model states that the probability of any shopper choosing a particular retail center is equal to the ratio of the utility of that center to the sum of utilities of all potential competing centers in the system (Huff 1964, p.37)0 Specifically, the utility or attractiveness of a center is directly related to the size of the center and inversely related to the distance separating consumers from the center.


Huff's model is probably the most parsimonious specification of modern theory-based approaches to the study of consumer spatial behavior. Earlier gravity models (Reilly 1929; Converse 1949) were specified at an aggregate level and were deterministic in nature. In contrast, Huff specified a multiplicative utility function with two variables, selling space and travel time. These two variables clearly act as proxies for the principal constructs of Central Place Theory (Christaller 1933; Losch 1954 - the importance of a center and economic distance. Thus 9 the theoretical justification of Huff's model can be found in Central Place Theory (Huff 1981).

Another major strength of the model is its inclusion of the effects of competition on the behavior of the shopper. This, by itself, adds much credibility to the model. By constructing probability contours, Huff's model also explicitly allows for the occurrence of irregularities of trading areas (Huff 1964).

Huff's model also survived much empirical testing since its formulation (Huff 1962; Lakshmanan and Hansen 1965; Bucklin 1967a,b; Brunner and Mason 1968; Pacione 1974; Thomas 1976; Stanley and Sewall 1976; Lieber 1977; Turner and Cole 1980; Nevin and Houston 1980; Gautschi 1981). It is also interesting to note that in spite of the problems surrounding the calibration of the model, the A value in Huff's model has been empirically verified in many studies (Carrothers 1956; Huff 1962; Forbes 1968; Bucklin 1971a,b; Haines et al. 1972; Young 1975; Stanley and Sewall 1976). In general, they tend to support an empirical value of about 2.0 for normal household shopping despite various calibration methods used (Wee and Pearce 1984).

Huff's model is not without weaknesses. First, the model assumes that consumers with comparable socioeconomic characteristics will depict similar retail center patronage and that there are no internal differences of significance within the area of analysis.

Second, it is interesting to note that Huff's competitive system includes all potential retail centers in that system (Huff 1964, p.37). In other words, the basic see of shopping area choice alternatives is assumed to be spatially accessible to all consumers without taking into account possible other factors that might affect the choice of shopping areas. Thus, the use of the basic set in the model is similar to what urban geographers labelled as "store opportunity set" in store choice behavior (Marble and Bowlby 1968) and what marketers labelled as "awareness set" in brand choice behavior (Campbell 1973; Narayana and Markin 1975; Hawkins et al 1980). Subsequent studies have continued to apply Huff's model in the same way (Stanley and Sewall 1976; Nevin and Houston 1980). While this approach may be appealing when there are only a few recognizable shopping centers within a city, the situation becomes less defensible when there are many shopping centers with varying degrees of consumer patronization. Thus, should a shopping area which a consumer patronizes once a year or even once in two years be included with another which he patronizes once every month? What criteria should be used for inclusion or exclusion of shopping centers in the competitive system? Clearly, if all shopping areas are included, the model may bear little relationship to actual consumer patronage patterns. This is because consumers may patronize different subsets of shopping areas within the basic set or they may patronize shopping areas that have not been included in the set. Using a priori assumption that the same set of area choice alternatives apply to all consumers may be necessary if one is interested to use the model in relation to predicting patronage behavior or estimating the size of trading area for a new center. The same assumption becomes highly questionable when one is also interested to explain patronage behavior among an existing set of shopping areas.

The problem of specification of what centers to be included in the set is well articulated by Gautschi (1981):

"In addition to the potential bias resulting from omitted variables, bias may stem from an improperly specified choice set ... "

This problem is further compounded by socioeconomic factors. Mobile shoppers, for example, may visit many centers within the city, or take advantage of car-oriented out-of-town centers if available, whereas other shoppers who are spatially relatively confined will be more dependent on local shopping facilities. In essence, Huff's model is still applied from a retailer's point of view.


One way of overcoming the specification problem in the competitive system of Huff's model is to allow the consumer to specify his/her choice set of shopping centers, as opposed to an arbitrary imposed set from the retailer's perspective. The choice set can be defined as those shopping areas that the consumer chooses to patronize over a certain period of time. Thus, it will resemble the evoked set concept that is used in brand choice research. The proposed model that incorporates the concept of choice set may be expressed in the general form:



Pij = the drawing power of shopping area j to consumer i;

Sj = the attraction of shopping area j;

Dij = the disincentive of travelling to shopping center j for consumer i;

{J}i = the index or choice set for consumer i, where {J}i = {1,2,3, ... n};

l = an exponent value.


The purpose of this study is to empirically test whether the proposed model will outperform Huff's model.

Research Site and Shopping Areas

A city in southwestern Ontario was used as the research site. The size of the city (population of 284,000) plus its traditional role as a test city for many market research studies makes it ideal for the nature of this study. Besides, in terms of membership, the city has the largest Downtown Business Improvement Area in Canada.

In total, 15 shopping areas have been included for this study. The criteria for inclusion were that the area should have at least 100,000 square feet of retail selling space and that it must have some form of management promoting it as a business entity. It was not necessary that the area be a planned center. The choice of 100,000 square feet as the cut-off for size was consistent with the findings of Turner and Cole (1980) who concluded that gravity models are more suitable for large and medium shopping areas.

Basic data on each of the shopping areas, including their retail selling space, were obtained from several secondary sources. The 1980 Canadian Directory of Shopping Centers provided the basic data for each of the shopping areas in this study, except for two areas. These data were verified and updated with the respective management of each shopping area and planning officials of the city.

It is important to emphasize that the city stretches only 9.3 miles from east to west and 7.2 miles from north to south. Most of the shopping areas in the study have competitors within a two-mile range, and the majority of them are located within a 3.5 mile range of downtown. Even the two farthest shopping areas are within 4.5 miles of the core of downtown.

Applebaum (1966) in his study of supermarket trade areas showed that the drawing power of a store could extend beyond 2 miles. Brunner and Mason (1968) found that the most significant and consistent driving time dimension in delineating shopping center trading areas was at the 15-minute driving points, as 75% of each center's shoppers resided within this range. Interesting, though, was the fact that 25% of the shoppers were willing to drive more than 15 minutes to the center. In fact, their study showed that where suburban centers were concerned, a higher percentage of shoppers (almost 30%) drove more than 15 minutes to the center.

Considering the results of the two studies, and taking into account the relatively small size of the city, the very accessible transportation system, and that this study was concerned with shopping areas as opposed to individual stores, all 15 shopping areas could be considered as potential competitors to one another.


The proposed model was tested against Huff's model with regard to the shopper's behavior toward the downtown area for non-grocery shopping. The dependent variable was operationalized as the number of actual trips (and dollars) that was made in downtown as a proportion of the total trips (and dollars) to all shopping areas in the consumer's choice set over a two-week diary period.

Square footage of selling space was often used as a surrogate measure for attraction of the shopping area (Huff 1962, 1963, 1964, 1981; Bucklin 1971a, b) and had applied in many studies, including Stanley and Sewall (1976) and Nevin and Houston (1980), and was applied in this study as well.

For the disincentive variable (Dij), distance was used instead of travelling time as it was felt that the former was a more objective measure. Specifically, crow-flight (straightline) distance was adopted after close study of the map of the research site which showed that there were no major obstacles within the city. The distance was measured from the consumers place of work if the majority of trips originated from and ended at the place of work. Otherwise, it was measured from the consumer's home. Thus this method of measurement took into account, in aggregate, trips' origin and end.

Finally, the X value was fixed at 2.0. In doing so, the authors had chosen not to consider the calibration issue, in light of the fact that there are many different methods of calibration and that the issue is still fraught with problems (Wee and Pearce 1984). There is considerable empirical support for using a X value of 2.0 for ordinary household goods shopping when the distance between competing shopping areas is not very great, and when shopping trips involve travelling to community or regional shopping areas (Reilly 1929; Carrothers 1956; Huff 1962; Forbes 1968; Bucklin 1971a, b; Young 1975; Stanley and Sewall 1976). Other researchers have also used the value of 2.0 in their studies (Huff and Lutz 1979; Nevin and Houston 1980). Thus, this study has opted to apply a model that has more operational and practical relevance to the manager, rather than engage in an academic pursuit that may have little value to Practitioners .

Data Collection and Response Rates

The data for this research were obtained as part of a large scale survey designed to obtain various information that helped to provide a better understanding of consumer spatial shopping behavior.

The survey required the respondent to complete an eight-page questionnaire and keep a two-week diary that recorded information on shopping trips and expenditure. Dillman's (1978) "Total Design Method" was closely followed in designing and implementing the survey. Initial contact letters, personally addressed to the female heads of households whenever possible, were mailed to 2070 residences in the city. A telephone call followed a few days after the letter. Of the 1269 principal shoppers reached by telephone, 823 agreed to participate in the study. A total of 679 returns, representing 82.5% of those who agreed to participate, were received. Of these, 482 respondents completed both the questionnaires and diaries and they formed the usable data-base sample. The return rate was equivalent to 58.6% of those who agreed to participate or 38.0% of those reached by telephone. Considering the level of difficulty of the survey instruments, the return rates were considered very satisfying.

Non-Response Bias

Owing to the use of two research instruments in this research, non-response bias was determined in two ways. For those people who refused to participate in the study, three demographic questions on age group, educational level and years living in the city were asked over the telephone. The results of the difference of means test of the non-participants against the data-base sample showed that there were no significant differences with regard to the length of residence in the city and the education level. The only significant difference was that of age. Considering the nature of this study, the results were not surprising as older people tend to have more difficulties with their seeing and writing capabilities and thus tend to shun away from participating (Dillman 1978, p.53). In fact, the refusal rate was 42.1% for those people over 55 years of age.

As this study involved completion of both the questionnaire and diary, non-response bias was further assessed between those respondents who completed only the questionnaire and the data-base sample. Comparison between these two groups were made along 7 criteria -- age, education, Siegel's (NORC) job prestige scale, income, years living in the city, years living at the present address, and the number of shopping areas visited over the last three months. The only significant difference, using the difference of means test, between these two groups, at the conventional 5% level of significance, was that of educational level. Again, this result was not unexpected. It was possible that those participants with lower level of education had more difficulty in responding to both the questionnaire and diary.

Taking into account that there were no significant differences within each of the two sets of comparisons that were discussed above, it was concluded that non-response bias was definitely not a problem in this study.


Since all the variables were measured at least on interval scales, multiple regression was selected as the appropriate analytical technique.

Two common criteria were used for the selection of the better model. These were the value of R-square achieved by the least squares fit and the value of the residual mean square. In addition, a third statistic which has gained popularity in recent years, the Mallows' Cp statistic (Mallows 1973; Draper and Smith 1981, pp.229-302) was also used. Basically, the Mallows' Cp statistic involves comparing the actual Cp value with the expected Cp value. The criterion for deciding the better model is the Cp value that is closer to the E(Cp) value as it would indicate an unbiased model in which the equation fits the actual data better.

The results are shown in Table 1. With regard to the. trip data, Huff's model attained an adjusted R-square of 0.178, a residual mean square of 0.0719 and a very high Cp statistic of 56.57. In contrast, the proposed model had a vastly improved adjusted R-square of 0.253, a lower residual mean square of 0.0654, and a much lower Cp statistic of 8.00 which was closer to the E(Cp) value of 2.00. The proposed model thus outperformed Huff's model on all three criteria. The superiority of the proposed model was also clearly reflected when the two regression equations were compared. The proposed model had a higher beta value of 0.504 compared to 0.424 for Huff's model.

Similar patterns of results were shown for the expenditure data on downtown. Huff's model showed an adjusted R-square of 0.138, a residual mean square of 0.1021 and a Cp value of 41.18. The proposed model recorded an increase of about 0.06 for the adjusted R-square to o.197, a lower residual mean square of 0.0952, and a much lower Cp value of 6.07. The beta coefficient of the proposed model was also much higher.

Examinations of the residual plots show that while both Huff's and the proposed models were slightly skewed positively, they did not affect the robustness of the regression analysis (Snedecor and Cochran 1967; Bohrnstedt and Carter 1971; Pedhazur 1982, p.34-36).

Double cross-validation of the best fit regression model (Lord and Novick 1968, p.285; Mosier 1951) was carried out to determine the stability of the proposed model and to ascertain whether the shrinkage in R-square was serious. The regression equations derived from the split samples are shown in Table 2. The results show that the Beta values, significance levels and R-squares are very similar for the trip data, attesting to the stability of the proposed model. While some shrinkage is noted for the regression on the expenditure data in terms of double cross-validation, the model still performs very well in terms of cross-validation.




In their review of urban consumer behavior, Shepherd and Thomas (1980, p.27) said of Huff's motel:

" ... given the potential practical value of the model, it is rather surprising that little research effort has gone into attempts to refine the original formulation in the practical context of retail planning within the city. Perhaps this represents a worthwhile direction for further research effort."

This study, besides responding to the above comment, serves to provide empirical evidence supporting the use of the concept of choice set in predicting and explaining consumer shopping behavior.

In order to better understand the problem of identifying potential competing shopping centers in Huff's model, the number and type of shopping areas visited by the principal shoppers during the entire study period were tabulated. Table 3 shows that consumers did not patronize all the potential competing shopping areas. Judging by the range and variance of the number of shopping areas visited, and the frequency in which each shopping area was included in the consumer's choice set, it was apparent that the set of shopping areas visited (choice set) varied from consumer to consumer. In general, the number of shopping areas within the consumer's choice set appeared to be around 6.0, as indicated by the mean of 6.55, mode of 6.0, and median of 6.36.





Many factors such as individual socio-demographic and psychographic differences, and the consumer's mobility and accessibility to shopping areas, could all have affected how and where the consumer shopped. While this research did not attempt to identify which of these factors did have an impact on the selection of shopping areas, the choice set intuitively acted as a surrogate measure that took into account such differences among individuals and other factors that could have affected their shopping behavior.

It was also interesting to note that the larger the mass of the shopping area, the more likely would it be included in the consumer's choice set (Spearman correlation coefficient of 0.7131, significance = 0.001; Kendall correlation coefficient of 0.5550, significance = 0.002). In addition, there was also a highly significant association between the frequency in which a shopping area was included in the consumer's choice set and the frequency in which the area was identified as a most-shopped area (Spearman correlation coefficient of 0.7464, significance = 0.001; Kendall correlation coefficient of 0.6381, significance = 0.001).

While using the proposed model may require more research, especially in terms of collecting data directly from the consumers, the process is not as complicated and difficult as it may seem. The research instruments can be simplified to that of a questionnaire alone. In fact, based on this study, using the proposed model even had a distinct advantage over using Huff's model as far as the distance measurement was concerned. Fewer distance measurements were needed for the proposed model as the respondent did not patronize all potential shopping areas. The average was six shopping areas in the choice set while there were 15 shopping areas in Huff's model.

Using the proposed model has two other advantages. First, it allows the user of the model to clearly identify which are the actual competing centers from the consumer's point of view. The user of the model will also be able to isolate the more "serious" competing centers in that such centers would be included more often in the consumer's choice set.

Second, the inability to identify actual competing centers has very much restricted the use of Huff's model to predictive purposes only. In contrast, the proposed models as operationalized in this study, not only can be used as a predictive tool, but also for explaining consumer patronage behavior toward existing shopping areas. The stability of the proposed model in terms of predictive and explanatory purposes was clearly established when the model was tested by double cross-validation.

In view that the future trend is toward building more shopping centers and that traditional shopping belts or areas are increasingly getting organized as integrated business entities, the problem of identification of potential competing shopping areas will become very difficult if Huff's model were to be applied without any modifications. Huff's model will also become more tedious to use when the number of shopping areas increases, for example, imagine the number of distance measurements needed if there are 20 potential competing centers. In contrast, the proposed model uses the choice set concept and is likely to be unaffected by the increasingly number of shopping areas.

Finally, it is important to point out that the model, as tested, has been deliberately confined in a parsimonious way in order to compare it against Buff's model. Further refinements to the proposed model can still be made. Possible variables that could be added to the proposed model may include the effects of specific stores and products (or services) on the choice of shopping areas, and more elaborate constructs such as image of the shopping area.


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Chow Hou Wee, National University of Singapore, Singapore
Michael R. Pearce, The University of Western Ontario, Canada


NA - Advances in Consumer Research Volume 12 | 1985

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