Behavioural extensions to preference mapping: the role of synthesis

Food Quality and Preference 11 (2000) 349±359

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Behavioural extensions to preference mapping: the role of synthesis

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Sara R. Jaeger a,*, Ian N. Wakeling b, Halliday J.H. MacFie c a

Institute of Food Research, Norwich Research Park, Colney Lane, Norwich NR4 7UA, UK b 4 Argyle St, Kings Lynn, Norfolk, PE30 5RQ, UK c 99 Hampstead Rd, Bristol B54 3HW, UK

Received 30 September 1998; received in revised form 22 July 1999; accepted 25 July 1999

Abstract It is suggested to tackle unsolved methodological problems in preference mapping by taking account of the behavioural processes underlying preference formation. To this end an information processing model of preference formation is proposed. Within this model we particularly consider the process of synthesis, which is the way sensory information about product similarities and differences is analysed and processed. Although current applications of external preference mapping assume that consumers and trained judges synthesise sensory stimuli similarly, accumulating evidence in the literature suggests that this is not so. We, therefore, propose that analysing preference data in terms of a product space that accurately re¯ects how consumers see products will improve preference mapping methodology. Di€erences in synthesis are accounted for by applying sets of synthesis weights re¯ecting di€erences in the relative weighting given to each sensory attribute. An empirical analysis of sensory and preference data pertaining to eating apples supports the hypothesis that consumers use only a few key sensory attributes rather than synthesise a large number of attributes during preference formation. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Information processing; Procrustes analysis; Sensory evaluation and apples

1. Introduction Preference mapping (Carroll, 1972) constitutes a group of statistical techniques which are rapidly ®nding their way into mainstream sensory and market research. Results can, for example, help to decide which of several newly developed product formulations should go to market launch and provide valuable information about brand positioning and segmentation patterns for the product category under study. Despite the increased popularity of preference mapping, unsolved methodological problems remain. 1.1. Problems with internal and external preference mapping The two major problems with internal preference mapping, which refers to the analysis of preference data only, pertain to the restricting underlying behavioural $ This paper was presented at the Fourth Sensometrics Meeting (Copenhagen, 6±8 August 1998). * Corresponding author at present address: Hort Research, Mt. Albert Road, Private Bag 92 169, Auckland, NZ. E-mail address: [email protected] (S.R. Jaeger).

assumption about communality of perception and the limitations in computational models. Following Carroll (1972) the basic assumption underlying this type of analysis is that `di€erent individuals perceive the stimuli in terms of a common set of dimensions, but that these dimensions are di€erentially important or salient in the perception of di€erent individuals' (p. 107). From a behavioural point of view this assumption may impose restrictions and reduce the presence of those individual di€erences in perception, which a preference analysis seeks to account for. To a certain extent Carroll was aware of this problem, recognising that only when subjects use the common underlying dimensions di€erently will these be revealed by internal preference mapping. Computationally internal analysis is more or less synonymous with the vector model (Slater, 1960; Tucker, 1960), which represents stimuli as points and subjects as vectors in a common multidimensional space. In this space, vectors indicate the direction of increased preference for individual consumers. The analysis is similar to a PCA where the products are samples and the consumers are variables (e.g. Krazanowski, 1988). The aim is to ®nd a low number of dimensions which explain the largest proportion of variation in the consumers' scores and, therefore,

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represent the common conceptual dimensions underlying the data. However, a di€erent approach to internal analysis, which represents both stimuli and subjects as points in the stimulus space, is provided by the unfolding model (Coombs, 1950, 1964). Here di€erent subjects correspond to di€erent `ideal points', which represent their respective optimal preferences. Unfolding analysis is similar to multidimensional scaling using algorithms like MDSCAL, as presented by Kruskal (1964). The development of improved models for unfolding analysis, which started with the work of DeSarbo and Rao (1984), has removed part of the computational problems associated with older algorithms (Schi€man, 1979). Today, unfolding analysis is used in marketing, particularly for the analysis of consumer choice decisions (e.g. DeSarbo, DeSoete & Eliashberg, 1987; DeSarbo, Lehmann, Carpenter & Sinha, 1996; DeSoete & Heiser, 1993; Schmitt & Schultz, 1995). A recent application for the analysis of snack food preferences (DeSarbo, Young & Rangaswamy, 1997) suggests that the methodology may also be appropriate in the food area. Although internal preference mapping is a mature methodology, research to improve its performance continues. To assist interpretation of the preference dimensions it has become customary to project `external' information about the stimuli onto the internal preference map. While sensory pro®les measures are typically used (MacFie & Hedderley, 1993), this can be done using any product related measures. See DalliantSpinnler, MacFie, Betys and Hedderley (1996) and Greenho€ and MacFie (1994) for examples of this technique, which McEwan, Earthy and Ducher (1998) refer to as extended internal preference mapping. Newly developed test procedures for the number of signi®cant preference dimensions and how well individual consumers are ®tted by the internal model (Wakeling, 1996) are already ®nding application (e.g. Jaeger, Andani, Wakeling & MacFie, 1998; Monteleone, Frewer, Wakeling & Mela, 1998). However, one problem that needs further attention pertains to the identi®cation of segments, particularly in relation to analyses with a large number of subjects and/or when more than two preference dimensions need to be considered (Schlich, 1995). Attempts to overcome this and other problems associated with internal preference mapping have led to the increased application of preference clustering (e.g. Callier, 1996; European Sensory Network [ESN], 1996; Helgesen, Solheim & Nñs, 1997; McEwan, Earthy & Ducher, 1998; Schlich, 1995). The problems pertaining to external preference mapping di€er somewhat from those of internal preference mapping. External analysis is impaired by the reliance on sensory analysis to provide an appropriate representation of the product stimuli and the use of complex mathematical models. In external preference mapping, rather than analysing preference data only, these are

®tted to a stimulus space derived from other non-preference product information relating to the stimuli. Mathematically, external preference mapping corresponds to polynomial regression using the four linearquadratic models implemented in the PREFMAP program (Carroll, 1972). Analysis proceeds at the individual level, ®tting each consumer's overall preference to the external space. The reader is referred to Greenho€ and MacFie (1994) and McEwan (1996) for further background information on external preference mapping. For external analysis to be successful it is essential that the external stimulus space contains dimensions which pertain to preference. That is, it must provide a meaningful view of stimuli di€erences as perceived by consumers. Consequently, as a product space derived using descriptive sensory analysis pertains to product similarities and di€erences as perceived by trained sensory judges, but not necessarily to consumer preference, this practice may be less than optimal. Exploring whether product spaces derived from sensory judges and consumers are comparable, is equivalent to questioning whether consumers and trained judges perceive sensory stimuli similarly. A further question pertains to whether the di€erences and similarities between products identi®ed via descriptive sensory analysis correspond to the di€erences in preference as seen by a group of consumers. In our opinion, this is debatable. The external regression models are purely mathematically derived without any consideration for the underlying consumer behaviour, a fact that becomes apparent when considering the problems associated with interpreting preference structures. In particular, when the quadratic coecients associated with the complex elliptical and quadratic models are of opposite sign the ideal point becomes a saddle point. This implies that one external dimension optimises preference whereas the other minimises preferences. Interpretation of the underlying sensory properties driving preference consequently becomes very dicult (e.g. Schlich, 1995). As preference modelling using the complex elliptical and quadratic models frequently results in saddle-type ideal points, these models are used sparingly in practical applications (McEwan, 1996). 1.2. An information processing model of preference formation Touching upon some of the methodological problems outlined above, MacFie and Wakeling (1996) suggested that the emerging empirical problems may be attributed to the lack of satisfactory explanation of the underlying preference related consumer behaviour. Extending MacFie and Wakeling, we suggest that improvements in preference mapping methodology can be achieved by taking account of the behavioural processes associated with preference formation.

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In line with current theories of decision making in psychophysics, psychology, economics and marketing we visualise preference formation in terms of an information processing framework. Most theories of human information processing are based on the assumption that information from the environment is received, encoded and processed before a decision stage is reached for the output (e.g. Engel, Blackwell & Miniard, 1998; Foxall & Goldsmith 1994). In terms of the information encountered when tasting a food sample, we propose that sensory stimuli are detected and identi®ed before being further processed. The interpretation of information is envisaged as forming a mental overview of product similarities and di€erences. When deciding how much a product is liked, we suggest that consumers compare their perceptual representation of stimuli to a set of idiosyncratic rules governing preference. Lastly, this a€ective evaluation is transformed to a preference score. In psychophysics, the contemporary signal detection theory of human perception (Green & Swets, 1966; Swets, Tanner & Birdsall, 1961) view both the initial reception (sensitivity) and the subsequent evaluation (criterion) of the stimulus as determinants of the perceptual response (e.g. Luce & Krumhansl, 1988). In accordance with this information processing representation of human perception, the importance of cognitive processes in sensory perception has received more acceptance in recent years, and evidence that perception is guided by both sensory and non-sensory processes is accumulating in the literature (e.g. Ashcraft, 1989; Booth, 1995; Dalton, 1996; Zellner, Bartoli & Eckard, 1991). Discussing the processes involved in sensory perception of food stimuli Booth (1994) summarised that `by means of brain processes, the assessors' minds have succeeded in turning information in the pattern of sensory input from the ¯avoured material into verbal or other forms of information in their recorded output' (p. 42). Contemporary models of consumer behaviour also rely strongly on information processing approaches. Decision making has been characterised in terms of eight successive steps, of which the ®rst ®ve (exposure, attention, comprehension, acceptance and retention) pertain directly to information processing (Engel et al., 1998; McGuire, 1976). For information to be processed and exert an in¯uence on choice and other behaviours, the consumer must ®rst be exposed to it. Then follows the selective reception process. Once received, stimuli pass through an attentional ®lter deciding which stimuli will be further processed. Limitations in processing capacity mean that consumers are very selective in what they pay attention to (Engel et al., 1998). Before the information that has penetrated to conscious awareness can impact consumer behaviour, it must be fully comprehended. Following McGuire (1976), this requires `to go beyond mere perception and e€ectively encode the

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information in one's meaning system so that one can grasp its import' (p. 306). Acceptance is decided by the assessment of whether the recipients of the information communicated agree with what they have comprehended. Once an outcome has been decided on, this is transferred to memory for future retrieval. In advertising, the traditional hierarchy of e€ects model (Lavidge & Steiner, 1961; Palda, 1966) hypothesises that promotional messages generate a cognition/ a€ect/conation response sequence. This is consistent with an information processing approach where information acquisition, perception and processing (cognition) precedes the evaluation (a€ect) of the available alternatives before forming a behavioural intention (conation). More recently van Raaij (1988) presented an information processing model to account for the economic behaviour of consumers, entrepreneurs and investors when making decisions under uncertainty. This model distinguishes between choice behaviour characterised by low and high levels of involvement. Only consumers highly involved in the decision process are proposed to cognitively elaborate the choice alternatives identi®ed through internal and external information search. Foxall and Goldsmith (1994) similarly emphasise this distinction characterising only highly involved consumers as carrying out information processing. From the outline of information processing models in psychophysics, marketing, advertising and economic psychology above, it is clear that these are all very similar. Basically, they portray an information processing consumer, who when exposed to information stimuli, attends to, processes and interprets it. By adopting an information processing approach to perception, this can be viewed as a process of reception followed by evaluation. In particular, it enables us to consider preference formation as a sequence of ®ve separate events (Table 1). When a consumer tastes a product sample his or her senses are activated through exposure to di€erent sensory stimuli. These sensory inputs are received and identi®ed to some degree during the stage of detection. This leads to the formation of an overall summary of the sample's sensory properties. We refer to this stage as synthesis. Taken together these three stages (activation, detection and synthesis) comprise the overall process of perception. During evaluation the perceptual representation of samples formed during synthesis is compared against a set of idiosyncratic rules that the consumer uses to determine how well samples are liked. Lastly, the overall product evaluation is transformed into a preference score. 1.3. Processes of synthesis An interpretation of external preference mapping methodology in terms of the proposed framework for

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Table 1 Information processing model of preference formation Information processing model (Engel et al., 1998; McGuire, 1976)

Preference formation model (Jaeger et al. 2000)

Exposure Achievement of proximity to a stimulus such that an opportunity exists for the senses to be activated

Activation Activation of sensory senses by exposure to stimulus

Attention Allocation of processing capacity to the incoming stimulus

Detection Identi®cation of single sensory characteristics

Comprehension Interpretation of the stimulus

Synthesis Formation of perceptual representation of product similarities and di€erences

Acceptance Persuasive impact of the stimulus

Evaluation Perceptual comparison of synthesis representation internal personal reference

Retention Transfer of the stimulus interpretation and persuasion into long-term memory

Scoring Transformation of the evaluation to a preference score

preference formation means that the external sensory space represents the perceptual summary of stimuli that consumers form during synthesis. The linear and quadratic regression models represent di€erent types of evaluative criteria consumers may use to decide how well samples are liked. Synthesis and evaluation are, thus, two important behavioural events that need to be considered carefully if improvements in preference mapping are to be obtained. In this paper we are concerned only with the process of synthesis. Particularly, we consider the behavioural implications for synthesis associated with current applications of external preference mapping. We have previously de®ned synthesis as the behavioural events associated with forming a mental overview of the sensory similarities and di€erences between products. Mathematically, a representation of this perceptual space is obtained from principal component analysis (or any other data reduction technique) of product pro®les generated by descriptive sensory analysis. In application, the external sensory space is typically

obtained by analysing either the variance±covariance or the correlation matrix of the sensory data. In behavioural terms these two computational approaches are associated with di€erent processes of synthesis. Principal component analysis of the sensory variance±covariance matrix implies that sensory judges and consumers synthesise sensory stimuli similarly, and that the trained panel provides an accurate representation of how consumers perceive the product stimuli. Correspondingly, analysis of the correlation matrix implies that consumers perceive all sensory attributes with equal intensity and that these contribute equally to the synthesised product summary (Table 2). Using a product space obtained from a trained panel implicitly assumes that this provides a good representation of product di€erences and similarities as seen by consumers. However, if this is not a case, the panel derived sensory map may not be optimal in terms of modelling consumer preference. In terms of the behavioural processes associated with preference formation

Table 2 Behavioural implication and calculation of di€erent types of synthesis weights Unscaled sensory weights

Scaled sensory weights

Unscaled preference weights

Key preference weights

Behavioural implication

Consumers and panellists synthesise sensory stimuli similarly

Consumers perceive all sensory stimuli with equal intensity

Consumers pay more attention to sensory attributes important for preference

Consumers only pay attention to the few key sensory attributes driving preference

Process of synthesis

Sensory attributes with largest variance contribute most to product overview

All sensory attributes contribute equally to product overview

Sensory attributes contribute to product overview in order of importance for preference

Only those key sensory attributes that in¯uence preference contribute to product overview

External product space

PCA of sensory covariance matrix

PCA of sensory correlation matrix

PCA of preference weighted PCA of key preference sensory covariance matrix weighted sensory covariance matrix

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this implies that consumers and trained judges synthesise sensory stimuli di€erently. Thus, it becomes necessary to use a di€erent representation of the product stimuli to that provided by the sensory panel. Moreover, this presentation must accurately re¯ect consumer perception. Numerous studies of consumer preference for food and beverages reported in the literature provide empirical support for the use of a representation of product stimuli based on the importance of sensory input for consumer preference. Generally, these studies suggest that not all sensory characteristics are equally important to consumers. For example, in a study of six food categories, Moskowitz and Krieger (1995) reported di€erential in¯uence of taste/¯avour, texture and appearance on overall liking. Similar ®ndings have been reported for a wide range of meat, poultry and ®sh products (Love, 1994). In terms of the behavioural implications for preference formation, this suggests that the perceptual product space consumers form during synthesis may be determined by the relative importance of sensory input for preference. That is, that the sensory attributes driving preference are more important during synthesis than attributes contributing less to preference. Taking the idea of di€erential in¯uence of sensory input for preference to its extreme suggests that some sensory inputs are crucial and others negligible in determining preference. Essentially, this implies that preference is driven by a few key sensory characteristics only. In applications of quality guidance models like the House of Quality (Hauser & Clausing, 1988) this is a key assumption. For example, using a modi®ed version of the House of Quality for the development of food products, Bech, Hansen and Wienberg (1997) focused on only ®ve in-mouth sensory attributes to guide the development of farmed smoked eel in accordance with consumer demand. In terms of preference modelling, di€erent types of synthesis may be thought of as di€erences in the relative importance or weight given to individual sensory attributes. Computationally these di€erences can be represented by applying di€erent synthesis weights to the panel derived sensory data. Particularly, the synthesis weights associated with principal component analysis of the sensory variance±covariance matrix all take the value of one, hereby re¯ecting the relative magnitude of each sensory attribute. The synthesis weights corresponding to analysis of the sensory correlation matrix are formed in such a way that all sensory attributes are given equal weight (i.e. all are scaled to unit variance). Di€erential importance of sensory input for preference may be represented by using a set of synthesis weights re¯ecting the relative contribution of individual sensory attributes to consumer preference. A set of synthesis weights giving very low importance to all sensory attributes except a few key sensory characteristics results in

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a stimulus space re¯ecting that consumer preference is determined by the variation in these key sensory attributes only. In Table 2 we refer to the above weights as unscaled sensory, scaled sensory, unscaled preference and key preference synthesis weights, respectively. So far we have outlined a framework for the analysis of preference formation which allows a critical examination of the behavioural assumptions associated with current applications of external preference mapping. Based on this framework it is clear that using an external product map that adequately represents the perceptual representation of stimuli consumers form during synthesis, is imperative for successful modelling results. As there is growing support for the view that consumers and trained sensory judges perceive and process sensory stimuli di€erently (e.g. Bech, Kristensen, Juhl & Poulsen, 1997; Munoz, Civille & Carr, 1992; O'Mahony, 1995; Stone & Sidel, 1993), we propose that improvements in external preference mapping can be obtained by using a representation of product stimuli which is in accordance with how consumers see product similarities and di€erences. That is, we hypothesise that application of preference derived synthesis weights leads to improvements in external preference mapping performance. 2. Materials and methods 2.1. Sensory and preference data The research hypothesis was tested using data from a sensory and preference study on 12 Southern Hemisphere eating apples. Further to the summary of ®ndings below, full details of the experimental procedures and results from this study are given in Dalliant-Spinnler et al. (1996). Peeled apple samples were pro®led using a vocabulary of 43 attributes relating to ®rst bite texture, ¯avour and texture during chewing, aftertaste and internal aroma and appearance. Principal component analysis of the correlation matrix resulted in a twofactor model accounting for 69.7% of the total variance. Samples were separated according to `green apple' vs. `red apple' characteristics along the ®rst dimension. The second dimension pertained to di€erences in texture. In parallel, 60 British consumers rated peeled apple samples for preference. Following internal preference mapping of the correlation matrix 27.9% of the total variance was accounted for by the ®rst, 16.5% by the second, 9.7% by the third, and 8.6% by the fourth preference dimension. Although Dalliant-Spinnler et al. (1996) provided an interpretation of the ®rst two pairs of two-dimensional internal preference maps (1. vs. 2. and 3. vs. 4.) relative to the underlying sensory variation in the product stimuli, signi®cance testing (see Jaeger et al., 1998; Monteleone et al., 1998) at the 10% level

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suggested that only the two ®rst dimensions were statistically signi®cant. Extended internal preference mapping identi®ed fresh ¯avour, acidic/sour ¯avour, juicy texture and crisp texture as the four sensory attributes that correlated most strongly with the preference map spanned by the ®rst two preference dimensions. The square root of the sum of the squared correlation coef®cient for these four attributes with the ®rst and second preference dimensions were: 0.87, 0.87, 0.71 and 0.72, respectively. Overall, correlation coecients ranged between 0.005 and 0.87 for the projection of all 43 sensory attributes onto the two-dimensional internal preference map. 2.2. Statistical analysis In accordance with the proposed framework for preference formation, the perceptual product summary created during synthesis may computationally be represented using the sample map derived from principal component analysis of synthesis weighted sensory data. For the sensory driven processes of synthesis this was achieved by principal component analysis of the sensory variance±covariance and correlation matrices, respectively. Similarly, representations of the preference driven processes of synthesis were obtained by principal component analysis of the variance±covariance matrix of the synthesis weighted sensory data. These were created by multiplying the preference derived synthesis weights, obtained using extended internal preference mapping (McEwan et al., 1998), by the mean sensory panel data. The square root of the sum of the squared correlation coecient between each sensory attribute and the dominant preference dimensions represents a weight re¯ecting the attribute's importance for preference (i.e. a synthesis weight). Further, the four sensory attributes most strongly correlated with the two-dimensional internal preference map were selected as the key attributes. The key preference synthesis weights were created giving these four attributes a weight of 1.0 and the remaining sensory attributes a weight of 0.1. Although the choice of these weights was somewhat arbitrary, the chosen values were intended to make the key attributes dominant and give the remaining attributes a small but negligible in¯uence on synthesis. The potential of synthesis weighting to improve existing preference mapping methodology was evaluated using Procrustes analysis and external preference mapping. Procrustes rotation (Gower, 1975, 1985) seeks to ®nd rigid body translations, rotations and re¯ections that move one con®guration of points to maximal agreement with a second con®guration in a least squares sense. Optionally, an isotropic scaling factor may also be applied. Thus, one con®guration (principal component scores from synthesis weighted sensory data) is shifted and rotated so that it matches, as well as possible, the

co-ordinates of another ®xed set of points (internal preference mapping con®guration). The outcome of the Procrustes rotation is evaluated using a measure of the remaining dissimilarity between the two con®gurations, namely the residual sum of squares (RSS). The smaller the RSS, the more similar are the two con®gurations. A graphical evaluation of results from Procrustes analysis was obtained by plotting the internal preference mapping con®guration and a rotated synthesis weighted sensory con®guration in the same space. For each product, preference and rotated synthesis weighted sensory product positions were connected with a line. This plot graphically illustrates the result of the Procrustes rotation, as the overall length of lines connecting individual products is proportional to the RSS value obtained. For example, when the two con®gurations are similar the RSS value is low and the lines connecting synthesis weighted and preference product positions are short. For external preference mapping normalised principal component scores from analysis of the synthesis weighted sensory data were used as external variables in the regression of preference data, as well as, rank 2 and rank 4 approximations to the preference data. A reduced rank approximation, obtained via singular value decomposition (Eckhart & Young, 1936; Good, 1969) of the full rank preference data, can be thought of as a principal component analysis which is used to reconstruct the original data matrix from the high variance components only. Geometrically, this corresponds to taking the projections of the original data points on the hyperplane described by the retained components. In e€ect this allows an examination of the di€erent synthesis weights under varying noise-to-signal ratios. A rank 2 approximation to the preference data was chosen to represent the two-dimensional model revealed by internal preference mapping. The rank 4 approximation resembled the four preference dimensions interpreted by Dalliant-Spinnler et al. (1996). All calculations were performed using Genstat 5.3 (Genstat, 1993) and SAS 6.12 (SAS, 1990). In Genstat, Procrustes analysis was performed using the ROTATE directive. Principal component analysis scores were normalised to unit length before Procrustes rotation, which was carried out without preliminary standardisation and isotropic scaling. External preference mapping was performed in SAS. 3. Results Procrustes rotations were performed using the ®rst two synthesis weighted sensory principal component scores and the ®rst two preference dimensions as input. For unscaled sensory, scaled sensory, unscaled preference and key preference synthesis weights, the following RSS values were obtained: 1.27, 1.78, 0.53 and

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0.43. This indicated that the preference derived synthesis weights provided a better approximation to the preference data than the sensory derived synthesis weights. The product space corresponding to unscaled sensory synthesis weights was more similar to the preference space than that derived from scaled sensory synthesis weights. Regarding the preference derived synthesis weights, the low RSS value obtained with the key synthesis weights suggested that the preference space could be adequately reproduced from a few key sensory attributes, namely the four sensory attributes (acidic/ sharp ¯avour, fresh ¯avour, juicy and crisp texture) driving consumer preference for Southern Hemisphere apples most. Fig. 1 illustrates the product spaces obtained using scaled sensory and unscaled preference synthesis weights in comparison to the preference space obtained from internal preference mapping. Note that the preference positions (grey circles) are the same in the two plots (the preference con®guration being ®xed in the Procrustes analysis). The sensory product positions, as they were derived from two di€erent types of synthesis weights, are not. In accordance with the Procrustes RSS values, the sensory space pertaining to unscaled preference weights (Fig. 1b) is clearly more similar (the length of the lines connecting sensory and preference product positions being comparatively short) to the preference space than the space derived from scaled sensory weights (Fig. 1a). For external preference mapping, the e€ectiveness of synthesis weighting was evaluated using the vector model only. Because the preference derived synthesis weights were obtained by projecting sensory information onto a vector model internal preference map, improvements in the number of consumers signi®cantly

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®tted by the external ideal point models were not expected. Preference data was regressed against external stimuli spaces spanned by the two ®rst dimensions from principal component analysis of synthesis weighted sensory data. As Dalliant-Spinnler et al. (1996) had previously interpreted the variation in the sensory data in terms of the two ®rst principal components, it was decided to include only two external dimensions in the analysis. The e€ect of eliminating noise and analysing only the structural information contained in the preference data was examined by using full rank and reduced rank approximations to the preference data. Values of explained variance and the number of signi®cantly ®tted (a=0.05) consumers based on the original, as well as, rank 2 and rank 4 approximations to the preference data are given in Table 3. Overall, external preference mapping of the full rank preference data using the vector model accounted for 32±38% of the total variance. Although varying only slightly, the variance explained by the di€erent synthesis weights suggested that a few more consumers could be ®tted using external dimensions based on preference derived rather than sensory derived synthesis weights. Compared to the full rank preference data, analysis of the rank 4 approximation to the preference data lead to improvements in the total variance explained. Although modelling results based on the di€erent synthesis weights remained largely similar, there was some indication that the key preference weights lead to better results than the unscaled sensory synthesis weights. Substantial di€erences in the total variance explained and the number of consumers ®tted were found only for analysis of the rank 2 approximation to the preference data. A comparison of results based on sensory derived synthesis weights with preference derived synthesis

Fig. 1. Graphical comparison of results from Procrustes rotation. Performance of scaled sensory synthesis weights vs. unscaled preference synthesis weights. Samples (Southern Hemisphere apple varieties) are identi®ed by numbers 1±12.

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Table 3 Results from vector mode external preference mapping Synthesis weight

% Var. expl.

% Sig. ®tted

Full rank Unscaled sensory Scaled sensory Unscaled preference Key preference

32 34 37 38

27 30 38 38

Rank 2 approximation Unscaled sensory Scaled sensory Unscaled preference Key preference

52 53 76 81

57 57 100 100

Rank 4 approximation Unscaled sensory Scaled sensory Unscaled preference Key preference

45 52 54 56

52 58 63 68

weights indicated notable improvements in modelling performance for vector model analysis based on the latter set of synthesis weights. 4. Discussion 4.1. Implications for the application of external preference mapping The indirect comparison of the four di€erent synthesis weights using Procrustes analysis clearly revealed that the product spaces obtained using preference derived synthesis weights were more similar to the internal preference mapping con®guration than product spaces based on sensory derived synthesis weights. However, as the preference derived synthesis weights were obtained by projecting sensory information onto the internal preference map spanned by the ®rst two preference dimensions, this result was not entirely unexpected. To overcome the bias associated with the comparison of synthesis weights using Procrustes analysis, these were also compared using vector model external preference mapping. In particular, as the internal map is not used in the external analysis this approach avoids comparing the internal map with the sensory space weighted in a manner so as to approximate internal map itself. External preference mapping showed that the di€erences between the synthesis weights with respect to variance explained and the number of consumers ®tted were only signi®cant for a low noise-to-signal ratio. For the rank 2 approximation to the preference data, a substantial improvement in modelling performance was achieved when regressing preference data against a product space based on preference derived synthesis weights. Based on the results from external preference mapping the hypothesis that

application of preference derived synthesis weights lead to improvements in external preference mapping was, thus, supported. When considering how external preference mapping can be best performed, this ®nding has several implications. In terms of the proposed framework for analysing preference formation, current applications assume that principal component analysis of the correlation (or variance± covariance) matrix of sensory pro®ling data adequately represents how consumers synthesise sensory stimuli. Contrary to this assumption the present results suggest that this is not so. Particularly, the results suggest that improvements in modelling performance may be obtained by regressing preference data onto a product space that more accurately re¯ects how consumers see product similarities and di€erences. The practical implication of this suggestion can be achieved in a 3-step procedure. The ®rst involves identifying the key sensory weights driving consumer preference (see later for a more in-depth discussion of this topic). Ideally this should be done within previously de®ned consumer segments. Preference weighted sensory data are obtained by applying these weights to the panel derived sensory pro®les, and principal components are extracted from the variance±covariance matrix of the synthesis weighted sensory data. The resultant principal component scores are used to de®ne the external space during external preference mapping. Before implementing the proposed modi®cations in industry, the limitations associated with this new approach must be carefully considered. First, the present ®ndings need to be validated with other preference data. Further replicating the present analysis with preference data containing three or more dimensions would provide a comparison to the current two-dimensional analysis and insight into the e€ects of stimulating the preference structure using the ®rst two preference dimensions only. In the event that several consumers are signi®cantly ®tted on the third (or higher) preference dimension, these may not be adequately accounted for if only the sensory attributes driving the ®rst two preference dimensions are considered. Validation of the preference derived synthesis weights is also needed. Synthesis weights that have been identi®ed in replicated preference studies within a single product category may be used with greater con®dence. This would be even more convincing if the preference weights could be con®rmed through another type of analysis than extended internal preference mapping. In terms of the present analysis, this would also remove some of the bias associated with the comparison of synthesis weights using Procrustes analysis. 4.2. Identi®cation of key sensory attributes Alternative ways of determining key preference weights need to be explored. Similarly to the extended

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internal preference mapping approach used in this study, new methods must allow identi®cation of the product characteristics that are most important for consumer preference. Discussing optimisation of food products guided by consumer evaluation Moskowitz and Jacobs (1988) advocate a category appraisal method for identifying the sensory attributes which trigger acceptance. Important characteristics (selected by the sensory scientist) are identi®ed from consumer ratings of intensity and liking of individual and category sensory attributes. Although this approach may appeal to many in R&D and quality control (e.g. MunÄoz et al., 1992), it may not fully capture the underlying consumer requirements. Further, Earthy, MacFie and Hedderley (1997) recently raised concerns that there are likely to be biases introduced if attribute type questions are asked concurrently with overall preference. Depending on the magnitude of such e€ects, results based on this type of approach may be nothing but artefacts, and the key sensory attributes may be wrong. Market driven approaches to developing food products in accordance with consumer demands have relied on frameworks like House of Quality (Hauser & Clausing, 1988) and quality guidance (Steenkamp & van Trijp, 1989). Within these, the key quality attributes re¯ecting consumer demands and their relative importance are usually derived using qualitative market research techniques like focus groups and structured indepth interviews. Grunert, Baadsgaard, Hartvig Larsen and Madsen (1996) generally recommend the focus group interview method (e.g. Casey & Kreuger, 1994; Greenbaum, 1986), and this has also been the favoured method in food related applications of the House of Quality (e.g. Bech, Hansen et al., 1997; Bech, Kristensen et al., 1997). Studies of quality perception for food products (Steenkamp, 1989; Steenkamp & van Trijp, 1989) have relied on group interviews, in-depth interviews and discussions with experts for the selection of key intrinsic quality cues. In line with van Trijp and Schi€erstein (1995) who advocate closer integration between marketing and R&D sensory methodology, we suggest that both approaches be used to identify the key product characteristics re¯ecting consumer demands. To gain further insight into the product perception process van Trijp and Schi€erstein suggest considering both product preferences and the product perceptions that underlie preferences. This opens the way to identi®cation of key preference attributes via interview and survey, as well as, cognitive perceptual techniques. Regarding the weighting of the sensory variables, one referee commented that it may be possible to identify the `optimal' synthesis weights using Partial Least Squares Regression. As the weighting of input variables in accord with their importance for the preference (response) variable is a key characteristic of PLS regression, this type of approach may be particularly

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appropriate. Further, viewing the problem addressed in this paper as a generalised regression problem, it seems there is an opportunity for ®nding a more elegant and mathematically ecient way of solving this modelling problem. Doing so presents an interesting challenge for future research. 4.3. Accounting for ideal point activity Regarding the formation of preference derived synthesis weights, a major drawback of the present approach is that these are based on a linear summary (internal preference map) of the preference data. While a majority of consumers tend to be signi®cantly ®tted by the vector model, a smaller proportion may be more adequately represented by an ideal point model. For example, MacFie and Wakeling (1996) report being able to ®t additional 20% of consumers in a preference trial by also using an ideal point model. Synthesis weights based on a vector model internal preference map may, therefore, not fully capture the sensory attributes driving preference for these `ideal point' consumers. To overcome this limitation it is possible to focus only on the key attributes driving preference and identify these using market research approaches. For some product categories there may be a speci®c concern that the majority of consumers re¯ect ideal point type preference behaviour (e.g. a trade-o€ between two dominant attributes like sweetness and acidity in orange drinks). If this is the case, it may be possible to establish an ideal point preference space and identify the key preference attributes in relation to this space. Using existing algorithms for multidimensional unfolding analysis (e.g. DeSarbo & Rao, 1984; DeSarbo et al., 1997) it may be possible to derive an ideal point internal preference space. In similarity to the present approach the key attributes driving preference may then be identi®ed by projecting sensory information onto this map. Rather than the attributes that are most highly correlated with the preference dimensions, the key attributes would be those in closest proximity to the majority of consumer points. Using our present data we tentatively attempted such an analysis. Encouraged by the possibility of using multidimensional unfolding to establish an internal ideal point preference space we derived a two-dimensional ALSCAL (Takane, Young & de Leeuw, 1977) solution using SPSS for Windows (SPSS, 1994). Much in accordance with the results reported by De Sarbo et al. (1997) this resulted in a degenerate solution with apple samples encircling the collapsed consumer ideal points. Thus, it appears that the need remains for developing and commercially implementing improved algorithms that can tackle the problem of `object/subject implosion' and render useful solutions. The computational representation of synthesis in terms of principal component analysis of synthesis

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weighted sensory data used in the present study implies that synthesis is a linear process. Whether this is true or not is, however, unclear. To empirically explore the possibility of non-linear synthesis would require comparing results obtained using traditional linear principal component analysis with results from non-linear principal component analysis or other non-linear data reduction techniques. Although such techniques exist (e.g. principal curves and surfaces: Hastie, 1984; Hastie & Stuetzle, 1989), the proposed framework for analysing preference formation makes it possible to account for non-linear e€ects during the stage of evaluation. In relation to external preference mapping di€erent evaluative functions are considered by using both vector and ideal point models. Although only the ideal point models, some of which are sparingly used in industry, account for non-linear e€ects, it is important to consider these. For more than one decade Moskowitz (e.g. Moskowitz, 1981, 1995; Moskowitz & Jacobs, 1988) has argued that consumer evaluation is directed by a quadratic rather than linear acceptance function. In terms of assessing the relative importance of sensory attributes on liking this means modelling linear, quadratic and possibly cross term e€ects. Solving the problem of deriving preference related synthesis weights outside the linear constraint currently imposed will allow full use of the ideal point models in external preference mapping. 5. Conclusions A review of the preference mapping literature revealed a number of problems with the existing methodologies. In an attempt to overcome some of these, an information processing model taking account of the behavioural processes underlying preference formation was developed. The empirical work focused on testing a key aspect of this model, namely the stage of synthesis. In accord with the proposed model we have demonstrated that consumers synthesise sensory information in a way that allows them to form a simpli®ed overview of product characteristics. To take this work further, the stage of evaluation must be considered next. Then, the model should be validated with data from other product categories. Further, there is a need to improve the way synthesis weights are identi®ed and calculated. The performance of Partial Least Squares Regression for this purpose should be considered. Acknowledgements This research was funded by the Danish Research Academy. The authors would like to thank DalliantSpinnler et al. (1996) for making the sensory and preference data available for further analyses.

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