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European Journal of Marketing,Vol. 33 No. 5/6, 1999, pp. 512-530.# MCB University Press, 0309-0566

Received May 1996Revised August 1996Revised March 1998

Image of suburban shoppingmalls and two-stage versus

uni-equational modelling of theretail trade attraction

An empirical applicationFrancisco Jose Mas Ruz

Faculty of Economics and Business Studies, University of Alicante,Alicante, Spain

Keywords Consumer behaviour, Image, Location, Malls, Retailing, SpainAbstract The main objective of this research is to examine the nature of the image of shopping malls and to contrast the reliability of two models that analyse the attraction of retail trade; in thefirst model, image, distance and preference are considered; whereas in the second, preference isomitted. The initial hypothesis is that the apparently lower power of attraction of the image,compared to that of the distance, may be justified, in some way, by the modelling of a relationshipthat omits preference. The methodology applied uses a variety of multidimensional techniques toidentify image dimensions, together with two focuses, the two-stage versus the uni-equational, todefine retail trade attraction. As a result of the application in the suburban commercial setting of Alicante, three image dimensions are detected in the malls, as well as the superiority of the uni-stage modelling in which the influence of preference on retail attraction is omitted.

IntroductionThe existence of intra-urban shopping areas, understood as intermediate levelretail entities that lie somewhere between the individual establishment and thecity (Bucklin, 1967), implies another level of decisions about retail attraction forthe consumer. In this sense, consumer choice of the place to shop implies adouble choice, that of a shopping mall and that of a specific establishment.

Concentrating first on the former, and from an investor's perspective, theproximity of other trade establishments is a determining factor in deciding onthe location of a new sales point (Bromley and Thomas, 1989). In fact, few retailestablishments exist as isolated entities. The synergies produced by theproximity of numerous shops, the legal restrictions on possible locations for

retailers, and the limited availability of attractive areas, tend to encourage thegrouping of retail outlets in relatively compact shopping centres. These factsmay reduce the possibilities of location to a small number of potential places,consisting of heterogeneous groups of individual establishments, which, in theopinion of Nelson (1958), are explained by means of the principles of ``accumulative attraction'' and of ``compatibility''.

The term ``shopping mall'' may mean either a coherent, planned andcontrolled group of establishments, with its own management and control of competition, or rather, the concentration of retail establishments, each one

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Table I.Probabilistic modellingof retail attraction

Lineofresearch

Variables

Methodology

Strengths/weaknesses

Outstandingauthors

Original

Sizeofestablishmentand

distancefromconsumer

Regression

Strength:utility

functions

aredefinedwithtwo

variablesofattractionand

dissuasion

Weakness:realityis

simplified

Huff(1963;1964;1966)

ExtensionofHuff's

model

Size,distanceandother

characteristicsofthe

salespoint

Regression(MCI)

Strength:simpleprocedure

ofestimationwithOLS

NakanishiandCooper(1974)

HansenandWeinberg(1979)

JainandMahajan(1979)

GhoshandMcLafferty(1982)

Multidimension.A.

Regression(MCI)

Strength:retailimageis

definedasa

multidimensional

phenomenon

StanlyandSewall(1976)

DoyleandFenwich(1974-1975)

Logitmodels

Strength:functional

exponentialformwith

smallernumber

of

hypothesesand

better

estimationswithOLS

Arnoldetal.(1980)

MillerandLerman(1981)

ReckerandSchuler(1981)

LouviereandWoodworth(1983)

Notes:OLS=Ordinaryleastsquares;MCI=Multiplicativecompetitiveinteractionmodel

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depends on size, measured in terms of the sales surface area of centre j, S j , andthe distance between the place of residence of individual i and the centre j, T ij (Huff, 1963; 1964; 1966; Huff and Batsell, 1977; Huff and Rust, 1984). A greatersales surface would increase the probability of a centre being chosen, whereaslonger travelling time would reduce it.

P ijU ij

n

j 1U ij

S jaT ijn

j 1S jaT ij

where,

P ij = the probability of consumer i choosing shopping mall j from npossibilities;

= sensitivity parameter which reflects the effect of travelling time fordifferent types of shopping trips.

Despite the fact that this model provides interesting information on theestimation of probabilities in retail attraction, it was criticized for simplifyingreality by not considering other attributes that exert attraction or rejection onbuyers. Some authors proposed that the retail image perceived by the consumeris a multidimensional phenomenon in determining their choice (Doyle andFenwich, 1974-1975; Stanley and Sewall, 1976) and that the factors of distanceand size are not always the best indicators for predicting retail attraction.

Likewise, other authors attempt to explain retail trade attraction by priorexamination of the relationship among the preference for a particular centre, its

image and the distance from it (Howell and Rogers, 1980; Hauser andKoppelman, 1979). Along these lines, Reibstein (1978) suggests, in theparticular case of brand choice, that the apparently lower power of attraction of the image as opposed to the distance may be justified, in some way, bymodelling a relationship which omits preference.

This problem led to the development of extensions of Huff's model,including new variables. In this line of generalisation, Nakanishi and Cooper(1974) propose an alternative formulation of the above, called the multiplicativecompetitive interaction model (MCI), extensively used for its simple estimationprocedure (Ghosh and McLafferty, 1982; Hansen and Weinberg, 1979; Jain andMahajan, 1979).

Likewise, in recent years, other alternative methods have been developed,among which the multinomial logit models applied by Arnold et al. (1980),Miller and Lerman (1981), Recker and Schuler (1981), Meyer and Eagle (1982),and Louviere and Woodworth (1983) stand out. These require a smaller numberof hypotheses than the ordinary least-squares and other classificationtechniques (Hosmer and Lemeshow, 1989). These are multiple discrete choicemodels, with a non-ordered dependent qualitative variable, which model thechoice behaviour of individuals between a finite number of non-orderedalternatives, where the qualitative dependent variable is associated with two or

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more alternatives, and the explanations include a variety of characteristics of the centres as expressed by the individuals (Gracia, 1988). McFadden (1974)demonstrates that the probability P ij of individual i choosing alternative j isgiven by the following expression:

P ijezij

n

j 1ezij

where zij is the vector of evaluations of consumer i regarding alternative j.Consequently, the modelling of distance, size, image and preference is

proposed, with different focuses, as an alternative way of analysing theattraction of shopping malls, which might allow us to avoid the simplificationof the original probabilistic models and to contrast the reliability of thedifferent approaches taken.

Prior empirical evidence of retail attraction in shopping mallsIn the particular case of shopping malls, relatively little research has beencarried out on choice and attraction. Furthermore, different approaches havebeen used (see Table II).

A first approach proposes the modification of Huff's model, taking intoaccount only the utility function of the malls ``evoked'' in different consumers.Wee and Pearce (1985) evaluate such a model by regression analysis, and showthat it fits better than Huff's model.

Another approach examines the attraction of shopping malls with differentextensions of Huff's model, to see if their predictive power improvessignificantly. Along these lines, Gautschi (1981) analyses (using regressionanalysis) the attraction of malls, both globally and individually, in relation toone of them, taken as a base, and considering the characteristics of theshopping mall and the means of transport to and from them. He also studies thebias caused by the set of alternatives selected by the researcher.

An alternative tendency analyses the attraction of shopping malls,incorporating their image as an extension of Huff's model. The aim is todetermine the image dimensions of the malls, the consistency among them, andtheir predictive power. Above all, they emphasize the fact that the determiningelements of image imply a complex relationship between their elements. Thisconditions the methodology employed, previously applying statisticaltechniques of grouping, such as the factor analysis. In particular, they specifythe image dimensions of each shopping mall by means of factor analysis, andexamine the influence of the components obtained, as well as that of the size/distance variable in an extended Huff model. The works of Nevin and Houston(1980) and McGoldrick (1992) are included in this framework. However, thisstudy does not take the size of the shopping mall into account, although it

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Table IIModelling of reta

attraction in shoppincentrLi

neofresearch

Variables

Methodology

Strengths/weaknesses

Outstandingauthors

Original

probabilistic

Sizeofcentreand

distancefromconsumer

Regression(OLS)

Strengths:variablesofattractionand

dissuasionareproposed.Theevoked

setofcentresisconsidered

Weaknesses:Realityissimplified

WeeandPearce(1985)

ExtensionofHuff's

model

Distance,characteristics

ofcentreandmeansof

transport

Regression(OLS)

Strengths:modellinginrelationtoan

alternativeasabase.Thebiases

derivedfromthecentresselectedare

examined

Gautschi(1981)

Size,distanceandretail

image

FactorAand

Regression(OLS)

Strengths:itconsidersthatimage

impliesacomplexrelationbetweenits

elements

Weaknesses:poorestimationsby

meansofOLS

NevinandHouston(1980)

McGoldrick(1992)

Wee(1986)

Distance,imageand

preferences

FactorAandSURE

Weaknesses:SUREapproachis

unsuitableashypothesisisnot

satisfied

HowellandRogers(1980)

Two-stagelogit

models

Strengths:exponentialmodelwhich

providesbetterestimationswithOLS

HauserandKoppelman(1979)

Distanceand

motivationalaspectsof

theindividual

FactorAand

Regression(OLS)

Weaknesses:poorestimationswith

OLS

Stoltmanetal.(1991)

Conceptual

Strength:retailattraction

and

reinforcement-affectmodelsare

combined

Meolietal.(1991)

Nonprobabilis

Motivationalaspectsof

theindividual

Discriminant

FactorANOVA

Factor-cluster

Centralplacemodel

Factor-regression

Weaknesses:probabilitiesarenot

predicted.Someauthorsuse

descriptivemethodologiesanddonot

defineutilityfunctions

GentryandBurns(1977)

WestbrookandBlack(1985)

Ghosh(1986)

Blocketal.(1991)

JarboeandMcDaniel(1987)

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includes certain personal features of the individuals involved. Another relatedstudy is that of Wee (1986). He, however, ignores the original variables of Huff'smodel, those of size and distance.

A fourth group of studies proposes a modelling for retail attraction based onthe consumer's preference for centres, together with distance and cognitiveimage dimensions. The works of Howell and Rogers (1980) and of Hauser andKoppelman (1979) fit into this category. This proposal implies a two-stageapproach, where a first equation estimates preference as a function of perceptual dimensions, while the second one analyses attraction based on thepreviously estimated preferences as well as on distance. However, the worksdiffer in considering or not, the influence of distance on preference in themethodology applied (SURE versus logit), as well as in their individual orglobal treatment of the centres.

Finally, a further line of research analyses the motivational aspects of

consumers which explain the attraction of malls. The starting point is thatsome shoppers will be attracted for purely economic reasons, others will beattracted for emotional reasons, while multi-purpose shoppers (Stoltman et al.,1991; Ghosh, 1986) will have a combination of these motives. Among theiremotional reasons, recreational activities (Bloch et al., 1989), search for ideas(Jarboe and McDaniel, 1987), the consumer's feelings about particular stores(Meoli et al., 1991), impulse, etc., stand out. Some studies also analyse theimportance of the area's attributes (Gentry and Burns, 1977-1978; Westbrookand Black, 1985; Stoltman et al., 1991), even as a function of the abovemotivations. However, the methodology used differs substantially in theseworks, ranging from the generalisations of Huff's model, by means of regression, to the use of discriminant analysis.

In short, the analyses carried out on the attraction of shopping malls differfrom one another in the group of retail entities studied, the variables selectedand the meaning given to each of them, and in the methodologies applied. As aresult of all this, the conclusions obtained also differ. It is therefore difficult todecide on the consequences of the determinating factors of the attraction of thecentres. However, the initial hypothesis of the fourth group of studies is that thelesser capacity of image as opposed to distance to explain attraction may bejustified, in some way, by the modelling of a relationship which omitspreference. In this article we propose a contrast of two focuses of the attraction

analysis. The first includes distance, image of shopping malls and preference,and in the second preference is omitted.

MethodologyThe research methodology developed in order to achieve the objectivesestablished covers the following stages: a determination of the group of imagedimensions of the malls with a range of multi-dimensional techniques, and thecontrasting of two focuses, the two-stage versus the uni-equational, in order tomodel retail attraction.

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First, the group of image dimensions perceived by the consumers of shopping malls is determined by means of the application of differentmultivariate statistical techniques, such as factor and discriminant analyses.

Factor analysis is based on the ratings of the attributes of shopping mallsprovided by the consumers. Their basic hypothesis is that there exists a limitednumber of perceptual dimensions that are related to the majority of originalattributes. In particular, the technique examines the correlations betweenattributes in order to identify these basic dimensions.

The calculation of the correlations between the ratings given to eachattribute is based on products and consumers (aggregating i and j for all),standardising them previously to minimise scale bias. The criteria whichdetermine the number of factors to be selected includes those factors with atotal explained variance percentage greater than 1 (that is, that their eigenvalueis greater than 1). These dimensions are named by examining the ``factor

loading'' obtained by varimax rotation, and are the estimations of thecorrelations between the ratings of the attributes and the perceptionmeasurements. Individual perceptions of the malls may then be discoveredfrom the ``factor scores'' ( xijd ) taken from the attributes' ratings.

Discriminant analysis also takes the attributes' ratings as a starting point.However, it selects the linear combinations of those attributes that bestdiscriminate between the malls. The dependent variable is the shopping mall,whereas the explicative variables are the ratings given to the attributes by theconsumers, and which have been previously standardized. The perceptions aremeasured by discriminating ratings ( xHijd ) or estimations of the perceptualdimensions that best discriminate between the malls, based on the attributes'

ratings. In the study, orthogonal or uncorrelated dimensions are used byapplying a varimax rotation.

Likewise, a comparison is made between these perceptual techniques interms of the interpretation of the dimensions, and their visualisation on a mapof the positionings of the market centres.

Second, we contrast the goodness of fit of two alternative models of shopping mall attraction. Distance, image and preference are included in thefirst model, whereas preference is omitted in the other.

In order to achieve this goal, we first examine a two-stage approach toattraction. Its general simplified form is presented in Figure 1. The fact that itallows us to research certain strategies, such as the improvement of the

Image/Perception Preference Attraction/Choice

Distance

Source: Adapted from Hauser and Koppelman (1979)

Figure 1General mod

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shopping environment, is one of its outstanding advantages. These will beespecially useful when relocation is not possible, as in the case of traditionaltrading areas (Hauser and Koppelman, 1979).

Howell and Rogers (1980) present a resolution procedure of this focus bydeveloping a model of multiplicative competitive interaction (MCI). It isestimated by means of the seemingly unrelated regression technique (SURE).However, the application of the SURE technique is extensively criticized for notquite satisfying the general specification given by Zellner (1962). Theinformation contained in its disturbances leads to inconsistent estimationsinsofar as the preferences constitute the endogenous variable in the firstequation and the exogenous variable in the second equation. Zellner and Lee(1965) propose an estimation procedure by generalised least squares, whichtakes into account the correlation between the disturbances of each equation inthe context of simultaneous estimation. However, this procedure does not solvethe problems of prediction outside the unitary interval included in the model of specified linear probability (Gracia, 1988).

On the contrary, Hauser and Koppelman (1979) offer a procedure which isbetter than the previous one in terms of the resolution of the two-stageapproach, taking as a starting point two uni-equational models. The first modelthey establish is that of preferences, which is mathematically defined by thefollowing expression:

pij $K

k 1

wkd ijk

where,pij = order of preference of individual i for mall j;

$ = indicates monotonicity;

wk = weighting of the importance of the k dimension;d ijk = perception of individual i in relation to variable k of mall j (in the

factor analysis d ijk xijd ; in the discriminant analysis d ijkxHijd The estimation of w k in the previous preference model is based on maximumlikelihood, in accordance with the conditional logit model proposed byMcFadden (1974). In this particular case, this monotonic technique estimates

the probability of a consumer classifying a shopping mall as his or her firstpreference. It is therefore called the first preference logit model.

Second, they use the conditional logit model with the aim of predicting theconsumer's choice, where the dependent variable is the frequency of visits andthe explanatory variables are the previously estimated preferencepij k wkd ijk and distance.

Once this two-stage focus is estimated, it is contrasted, on the one hand, withits goodness of fit in terms of the accuracy of its predictions, using criteriabased on the theory of information (Hauser, 1978): the preference test is the

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percentage of consumers who classify as first the shopping mall which themodel predicted as the first; the prediction test of the choice is contrasted bymeans of the increase in the percentage of uncertainty (entropy) explained by amodel resulting from adding the perceptual dimensions to another model basedexclusively on distance. On the other hand, this test allows us to contrast thehypothesis of the two-stage nature of retail trade attraction by estimating a solelogit model of revealed preferences. Its dependent variable is the frequency of visits and the explanatory variables are the distance and the perceptual imagedimensions.

Sample, data collection and variablesThe methodological process presented in the previous section is developedbelow for the specific case of consumers of four shopping malls of the city of Alicante with retail establishments of occasional consumption products. This isan interesting example for analysing retail attraction.

The four centres considered separately the central areas of the cities fromthose located on the outskirts. In particular, the ``Heart of Alicante'' is arevitalised central district, made up of a large number of specialised shopswhich have formed an association in order to defend their own interests. On theother hand, ``Maisonnave-Oscar Espla'' is located in another central urban area,though it consists of two department stores, and a large number of specialisedshops. Finally, the areas of ``Carreteras de San Vicente'' and ``San Juan''represent two centres of attraction which are easily accessible by road, both of which include a supermarket and several large shops of occasional-

consumption products.The basic information was obtained from a door-to-door survey, with astructured questionnaire, aimed at a sample of 177 individuals who participateactively in family decisions regarding shopping, in Alicante and San Vicentedel Raspeig during the month of November 1994. The sample populationconsisted of members of both sexes, 18 years or older, 10,0067 in Alicante and21,080 in San Vicente (IVE, 1994). The sampling was random poly-stage, andthe interviewees were selected by means of a procedure of random routes. Thesize of the sample guarantees a sample error of 7.5 percent with a level of confidence of 95.45 per cent (in the worst case p = q = 0.50). Likewise, thesample chosen is homogeneous in relation to socio-economic status, whichwould primarily solve problems of heteroscedasticity due to income, and wouldrestrict the scope of the study to the preferences towards certain shoppingmalls and to the income group included.

A detailed inspection of the information obtained allows various errors incertain interviews to be detected, and they are therefore eliminated from theanalysis. The number of interviews in the analysis was consequently reducedconsiderably. However, examining the characteristics of the remaining sampleled to the conclusion that it was reasonably representative of the objective

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population. In this sense, and with an identical level of confidence, the sampleerror was of 11.4 per cent for the 76 valid interviews in each equation, once thestatistic transformations of the regressions for each centre were carried out.

The variables used in the model were the following.The dependent variable in any choice model is a measurement of past

shopping behaviour in each centre. Specifically, it reflects the number of timesthat the respondent has shopped, for occasional-consumption products,(clothing, home furnishings and electrical appliances) in each of the centres,over the past 12 months. These absolute frequencies become relative from thetotal number of shopping trips of each individual during the above year(Gautschi, 1981). A ``shopping trip'' is considered to be any trip made to look foroccasional products, regardless of whether they are purchased or not.

The preference for a given mall is measured on a four-point scale, from themost preferred (1) to the least preferred (4), considering proximity/accessibilityas a constant.

The distance is measured by the average time spent travelling, as perceivedby the interviewee, from his or her place of residence to the shopping mall,using different means of transport.

A typical problem that arises in the research into preference and choice of shopping malls is the evaluation of their image components. That is, we cannotensure that the factors used in the image studies of individual establishmentsare appropriate for shopping malls. This is because some attributes of shopscan only be applied to malls if they have achieved success by creating agenerally consistent and cohesive image. Likewise, the mall has certainattributes of its own which are quite different from those of sales points, yet

common to the whole area.Taking these considerations into account, the following variables proposedby Gautschi (1981) are used to define the image of shopping malls: the varietyof products (size or center importance proxy), the professionalism of their salesassistants, the formality or informality of dress required of the shopper, thetranquillity of the buying process, cleanliness, ease of communication betweenestablishments, parking facilities, value for money, and opening hours (in theevenings and at weekends). These variables are specified by means of a seriesof affirmations with which the individual identifies him or herself, based onfive-point scale, in which a score of 5 points reflects total agreement and a scoreof 1 point the opposite.

Results obtainedIdentification of the image dimensions of shopping centresFirst, a principal components analysis with varimax rotation is applied to theimage attributes of shopping malls, with the aim of determining a reducednumber of uncorrelated factors, which may represent the originalintercorrelated variables. That is, they account for most of their totalvariability. The first three factors were extracted with a percentage of variancegreater than 1, the accumulated percentage being 61.4 per cent.

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Likewise, the application of the discriminant analysis with varimax rotationto the image attributes of the malls allows us to know the dimensions whichbest discriminate between them. In particular, this technique suggests threedimensions, the 1 2 test being significant at 1 per 1,000.

In order to interpret the underlying dimensions in the image structure, thecomposition of the factor loadings and the significant discriminatingcoefficients in shopping malls are studied (see Table III). The correspondingvariables are grouped and a name is chosen in accordance with the contents of each group.

In the factor analysis, factor 1, ``shopping environment and variety'', groupsthe variables of informality of dress, shopping hours, variety of products andcleanliness. Factor 2, ``parking'', is defined by parking facilities and low prices.Finally, factor 3, ``shopping environment and professionalism'', includes, aboveall, the variable of tranquillity in the buying process, and, to a lesser extent, the

professionalism of the sales assistants and the ease of access betweenestablishments.On the contrary, in the discriminant analysis, dimension 1, ``variety and

professionalism'', includes product variety as the most important variable, withless emphasis on sales assistant professionalism and shopping hours.Dimension 2, ``parking'', emphasizes the parking facility variable with lessimportance being given to accessibility among the different establishments.Finally, dimension 3, ``shopping environment'', is defined mainly by thevariable of the tranquillity of the shopping process and to, a lesser extent, bythe informality of dress and opening hours.

Despite the apparent similarities between the two models, importantdifferences arise in their interpretation. In particular, the factor analysis uses allthe attribute scales, while the discriminant analysis only does so with seven of the nine attributes, with only three being greater than 0.5. Consequently, andgiven the importance of market follow-up for managements, the discriminantanalysis relegates this to the study of a smaller number of strategies.

Another way of comparing the two techniques is by examining the visualmaps produced for each method (see Figure 2). These allow us to identify thepositioning of the different shopping malls in the market, their strengths andweaknesses, as well as their market opportunities.

A first glance at Figure 2 shows a certain consistency between the models

when the dimensions involved are very similar. For example, low scores areobserved for dimension 2, parking facilities, both in the Heart of Alicante aswell as in Maisonnave-Oscar Espla, while they are high in Carreteras de SanVicente and San Juan. The Heart of Alicante also shows a higher score indimension 3, shopping environment (professionalism). Regarding dimension 1,variety-environment (variety-professionalism), Maisonnave-Oscar Espla showshigher levels, whereas for the Heart of Alicante they are lower. In general, thesepositions are consistent with the prior beliefs about the image of the fourshopping malls.

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Table III.Comparison of perceptual models

Factoranalysis(factorloadings)

Discriminantanalysis(discriminantcoefficient)

Fundamentalattributes

Environment

andvariety

Parking

Environmentand

professionalism

Varietyand

professionalism

Parking

Environment

Productvariety

0.717

0.058

0.238

1.010

0.126

0.228

Salesassistantprofessionalism

0.440

0.240

0.569

0.449

0.219

0.239

Informalityofdress

0.725

0.095

0.067

0.239

0.234

0.374

Tranquility

0.061

0.190

0.880

0.034

0.079

0.942

Cleanliness

0.664

0.021

0.009

0.078

0.008

0.197

Establishmentcommunication

0.362

0.355

0.489

0.092

0.314

0.240

Parking

0.150

0.826

0.178

0.026

0.790

0.130

Prices

0.150

0.810

0.165

0.239

0.273

0.212

Openinghours

0.765

0.217

0.072

0.335

0.011

0.331

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Evaluation of the different choice models and of the preferences forshopping mallsFirst, the two-stage model proposed by Hauser and Koppelman (1980) isexamined: The first model they establish is the ``first preference logit'', which isestimated for maximum likelihood, in accordance with the conditional logitmodel. Likewise, they use the conditional logit model again to predict the

1.2

1

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

1

1.2

entroides of groups

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Factor scores

Discriminant analysis

Discriminating dimension 2

Shopping Malls

Discriminating dimension 1 Discriminating dimension 3

Key

Heart of AlicanteMaisonnave-O EsplaCtra San VicenteCtra San Juan

Factor analysis

Factor 2Shopping Malls

Factor 1 Factor 3

Key

Heart of AlicanteMaisonnave-O EsplaCtra San VicenteCtra San Juan

Figure 2Comparison

perceptual map

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consumer's choice where the dependent variable is the frequency of visits andthe explanatory variables are the previously estimated preference and distance.

Second, a revealed preferences model, which relates frequency of visit todistance and perceptual dimensions, is estimated.

Finally, in the following section, with the objective of contrasting thegoodness of fit of the different focuses used, a logit model which regresses thefrequency of visits with distance is proposed. Table IV shows the resultsobtained in each of these alternative approaches.

In general, for multiple choice models, the maximum likelihood estimators of the parameters follow a normal asymptotic distribution. Therefore the t statistic employed, of individual significance of the parameters, is distributedas a t of student. The estimated coefficients reflect the effect of a unitary changein an explanatory variable on the logistic transformations of the probabilitiesconsidered. The analysis of the joint significance of all the regressors, or in

other words, the evaluation of the explanatory capacity of these models, isconducted by means of the 1 2 test of likelihood ratio, where the null hypothesisis that all the coefficients are equal to zero. That is, the hypothesis that all thealternatives are equally probable is shown.

Table IV.Models of preferenceand choice (standarderrors in brackets)

First preference logit Revealed preference logit Distance logitExplicit variance Preference Visit frequency Visit frequency Visit frequency

Factor analysisFactor 1 0.327 ***

(0.880)0.500*

(0.287)Factor 2 0.2533 ***

(0.082)0.058(0.135)

Factor 3 0.201 **

(0.082)0.241

(0.178)Preference 1.515

(1.844)Distance 0.041 ***

(0.015)0.037**

(0.016)0.040***

(0.015)1 2 10.02** 7.74** 11.45** 7.06***

Discriminant analysisDiscr. dimen. 1 0.048

(0.078)0.308*

(0.184)Discr. dimen. 2 0.099*

(0.056)

0.105

(0.087)Discr. dimen. 3 0.130

(0.084)0.020

(0.151)Preference 1.343

(2.723)Distance 0.038 **

(0.015)0.037**

(0.016)1 2 5.46 7.31** 11.14**

Note: *** p < 0.01; ** p < 0.05; * p < 0.10

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The application of these tests to the evaluation of the discrete choice modelsand the interpretation of the coefficients allow us to conclude, based on theresults obtained, that distance is a good predictor of the choice of a mall in anyof the models analysed. It is significant in all of them at a level below 0.05 or0.01. Practically all of the models are statistically significant at a level below0.05. This appears to reflect that the consumers' choice mechanism is coveredin the functional specification of the logit model.

If one considers the focus denominated ``first preference logit'', it is detectedthat the model which is based on the factorial dimensions has a highexplanatory capacity (the 1 2 test is significant at a level below 0.05), with thefirst and second image factors standing out as good predictors of preference.On the other hand, the model with discriminating dimensions has littleexplanatory capacity. This seems to favour factor analysis as opposed todiscriminant analysis.

Finally, the detailed examination of the logit model of revealed preferencesshows that distance is significantly different to zero at a level below 5 per cent,while the first factorial or discriminating dimension is only so at a level below10 per cent.

Goodness of fit of the modelsIn addition to the contrasts carried out in the previous section of the goodnessof fit of the different models, the prediction tests of preference and choice (seeTable V) are examined. The preference test is the percentage of consumerswhose first choice was the shopping mall which the model predicted would befirst; the prediction of choice is contrasted by means of the increase in the

percentage of uncertainty (entropy) explained by a model resulting fromadding the perceptual dimensions to another model based exclusively ondistance (see Table IV).

Taking the choice prediction test as a starting point, the hypothesis of thetwo-stage nature of the model of commercial attraction may also be contrasted.This requires the estimation of a revealed preference logit model (see Table IV),whose dependent variable is frequency of visits and whose explanatoryvariables are distance and perceptual image dimensions.

In relation to the predictive preference test, Table IV shows that 40.8 per cent(31/76) and 35.5 per cent (27/76) of the consumers classified as first the

Table VPredictive tes

Preference Choice

Factor analysis1st preference logit 40.8 1.2Revealed preference logit 7.7

Discriminant analysis1st preference logit 35.5 0.4Revealed preference logit 7.1k

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shopping mall which the model predicted would come first, for the factorial anddiscriminating dimension models respectively. Its maximum value is 100 percent, although the majority of empirical studies do not come close to such apercentage of success. Instead, the measurements obtained should be comparedto those resulting from a purely random assignation where all the locationshave an identical probability of being chosen (Hauser, 1978). In this particularcase it would be 25 per cent.

In relation to the choice prediction test, Table V presents the percentage of uncertainty explained, related to a model based exclusively on distance. In thissense, it is clear that the first preference logit models only predict poorly withregard to distance, by adding a very small amount of uncertainty in theprediction of choice. On the contrary, it may be concluded that the revealedpreference models are more adequate than first preference logit models given thestatistical improvement produced regarding distance. Total uncertainty wouldresult in aggregating 12.4 per cent to themeasurements offered in TableV.

Likewise, the relationship of the proportionality which exists betweenexplained uncertainty and the statistic 1 2 (Hauser, 1978) allows us to contrastthe significance of the choice models. Specifically, after adjusting the frequencyof visits, 2N * percentage of relative uncertainty follows an 1 2 if the nullhypothesis (model based on distance) is a special case of the contrasted model(it aggregates the perceptions to distance). The degrees of freedom are given bythe difference in the number of variables. The results obtained allow us toconclude that all measurements of uncertainty are significant at a level of 0.01.

ConclusionsThe implication that the original probabilistic components, size/distance,

image and preference for shopping malls that distinguish different urban areasare three important elements to be considered in any analysis of retailattraction, has allowed us to analyse the phenomena of retail trade attraction inthe urban setting of Alicante.

The methodology applied uses a variety of multidimensional techniques foridentifying the dimensions of the image, as well as different logit focuses, thetwo-stage versus the uni-equational, to define retail trade attraction.

As a result of the empirical application employed, the existence of threeimage dimensions is detected in the shopping malls examined in the city of Alicante. Likewise, the evaluation of discrete choice models and theinterpretation of their estimated coefficients allow us to conclude that distance

is a good predictor of the choice of a centre in any of the models analysed. Theanalysis of goodness of fit of the different approaches to the modelling of attraction shows the superiority of revealed preference models (uni-equational)over first preference logit (two-stage), given the statistical improvement itaffords regarding distance.

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