physical and sensory data in food acceptance studies

physical and sensory data in food acceptance studies

Food Quality and Preference Food Quality and Preference1988 1 (I) 25-31 ~ Longman Group UK Lid 19880950-32931881011040251503.50 Received18June1988 Acc...

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Food Quality and Preference Food Quality and Preference1988 1 (I) 25-31 ~ Longman Group UK Lid 19880950-32931881011040251503.50 Received18June1988 Accepted210ctober1988

A A Williams,* C A Rogerst¢ and A J Collinst *Sensory Research Laboratories Ltd., 4 High Street, Nailsea, Bristol BSI9 1BW, UK tDept, of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK ePresent address: United Kingdom Transplant Service, Southmead Road, Bristol BS10 5ND, UK

Relating chemical/physical and sensory data in food acceptance studies

Abstract

Introduction

To understand food acceptance requires the integration of objective descriptive sensory data with consumer acceptance information and chemical/physical data. T h e paper briefly discusses sensory and chemical/physical information in the context of food acceptance. It stresses the need that such information should be as meaningful as possible and provides an example of the potential benefits gained from applying generalised Procrustes analysis to rationalise the sensory data. Such treatment can provide a more reliable representation of the inter-relationships between products, on the basis of their sensory properties, independent of descriptive terminology used. A number of the mathematical techniques available for investigating how such data relate to the complex stimuli found in foods are also discussed. By viewing the data as a vector space of variables salient features are highlighted; attention is drawn to the limitations of the more conventional regression and correlation approaches and the concepts behind alternatives, such as partial least squares regression. Reasons are given as to why the latter approach would appear to be the more suitable for relating sensory and chemical/physical data. The methods are illustrated using an example taken from work on wine.

Understanding the reasons for food choice is complex (Williams 1983a, 1983b, 1985, 1986, 1987; McEwan & Thomson 1988). If a food or beverage producer is to succeed in the market place he must be aware of his potential customers' likes and dislikes, their attitudes to his products and the various ecomonic factors which influence purchase. It is desirable that such information be related to production variables or to chemical and physical properties of a product; and in terms that the food technologist can understand and manipulate, and not vague descriptive terminology as is often the case. By approaching the problem in this way a producer can begin to build food quality into his product, and give it the same consideration as he does to availability of raw material, processing capability, energy requirements, etc. Such information facilitates the optimisation of product ranges, the successful creation of new products and the best use of advertising. Overall acceptability results from the integration of many factors. Some, like the sensory properties, are primarily intrinsic to the food or beverage, whereas others relate to the needs and attitudes of the consumer. A full understanding of t h e sensory aspects of food and beverage acceptance requires the integration of hedonic information with both objective assessments on how the product is perceived, and chemical and physical information on the product itself. By relating hedonic and objective information it is possible to

Keywords: food acceptance; chemical data; sensory data; regression modelling

26

Williams, Rogers and Collins

determine just how individuals perceive foods, and the influence each characteristic has on food choice. By adding extrinsic factors such as environment, advertising, packaging or production variables into this relationship, one can also determine how these influence perception, and hence acceptance. Only when the manufacturer has information of this nature which can eventually be related back to the chemistry and physics of the product concerned, can the scientist really and truly start to manipulate foods and beverages to optimise the critical factors influencing food choice. This paper addresses some of the problems encountered when one tries to interpret sensory information in terms of chemical and physical data. If meaningful relationships are to be obtained, the information that is being related must be as reliable as possible. With regard to the sensory data, multivariate statistical techniques, such as Procrustes analysis, can be used to abstract important dimensions and rationalise terminology. The chemical/physical data may also produce ambiguity, but more with respect to what is actually being measured, rather than how it is being described. Numerous mathematical techniques ranging from simple correlation to partial least squares regression (Martens & van den Burg 1985; Martens & Martens 1986) have been suggested as procedures for exploring relationships between sensory and chemical/physical data. By viewing the data as a variable space and using geometric representations to describe the procedures, we explore how some of these methods attempt to abstract relationships. Their limitations and favourable aspects are highlighted and reasons given why some methods may be more suitable for deriving sensory-chemical/physical relationships than others.

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We believe that the key to understanding the relationships between acceptance and sensory information and between sensory and chemical/physical data is the production of a sample or perceptual space, which reflects the relationship between samples, in terms of their perceived characteristics (Williams 1983b, 1985). Once this space has been derived, appropriate mathematical techniques can be used to place dimensions through it relating to acceptability, production or chemical/physical variables (Williams in press). One can also sup¢rimpose this space or appropriate acceptance dimensions through it, on a similar analytical space derived from analytical or physical

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are due to the data collection procedure and to isolate sub-groups of assessors who perceive samples in a common way. The objective descriptive data are then presented in a form that is most likely to deliver meaningful sensory-chemical/ physical relationships. Generalised Procrustes analysis is one technique which enables the underlying sources of variation, with respect to both terminology and the use of scales, to be rationalised before producing a sample space (Gower 1975; Arnold & Williams 1986). It also permits sub-groups of people who perceive the samples similarly, irrespective of how they score them, to be isolated. The technique operates by taking individual sample spaces, superimposing their centroids and then rotating, stretching and shrinking each of the spaces so that corresponding samples, as scored by each assessor, come as close together as possible (Fig. 2). By taking the centroid of each

information in order to determine the cause of significant characteristics (Williams et al. 1984). A sensory or perceptual space may be derived by one of three approaches: conventional profiling, free-choice profiling or similarity scaling (Williams & Arnold 1984). In similarity scaling the inter-sample distances are constructed directly from the similarity scores, whereas in conventional or free-choice profiling, each of the derived terms represents a dimension through the sample space. The score given for each attribute then defines the unique position of the sample in the space (Fig. 1), the distance between samples reflecting similarities and differences. However, people vary in how they perceive and score sensory characteristics in foods and beverages. Before relating sensory information to chemical/physical data it is important to explore the extent of this variation, to remove those aspects which

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Relating chemical/physical and sensory data in food acceptance studies

group of samples one can produce a consensus sample space, in which any possible confusion in the use of terms and variation in the use of scales has been removed. Also, by inspecting the scatter of individual samples about the centroid, one can discover the degree of agreement between the assessors and, if necessary, isolate sub groups who are perceiving samples differently. With conventionally-derived profile data, the use of rationalisation techniques such as generalised Procrustes analysis does not always improve the perceived inter-relationship of the samples. One example, however, where benefits were achieved, is illustrated in the case of a profile examination of four Beaujolais Nouveau wines, (Fig. 3). These wines were examined every month from December to April during 1984-85, using conventional profiling procedures and the language given in Table 1 (Eti6vant & Williams 1985). The sample plots, as illustrated in Fig. 3, relate to the first two principal axes, obtained from a principal component analysis (PCA) of the panel mean, and of the concensus data resulting from a rationalisation by generalised Procrustes analysis respectively. Although both analyses identified a major dimension which separated the samples on the basis of a 'cherryade' note, only after Procrustes matching could one dimension (principal axis 2) be associated with age.

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The extent of the chemical/physical information that may have an impact on the sensory perception of a product is enormous. It ranges from simple, general measurements such as pH to those which are very specific and rely on sophisticated instrumentation. A number of these and the sensory properties on which they have maximum impact, are given in Table 2. Because a plenitude of analytical data can be recorded on any particular product, it is usual to restrict any sensory chemical/ physical investigations to aspects that are most likely to have impact on the sensory properties of interest. For example, information on non-volatile compounds would be expected to relate more to appearance, texture and taste than aroma. However, care must be taken when making such assumptions. Non-volatiles, for example, can influence the way in which volatile components are released from a product and hence how they are perceived. Volatiles may have primary taste sensations or may have unpredicted effects upon the sensory properties (or blandness) of other volatiles. Non-mathematical rationalisa-

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Intensity Raspberry/Berry Blackcurrant/Ribena Syntheticcherryade Estery Diacetyl Creamy/Caramel/Vanilla Peppery/Spicy Vegetative/Green bean Sulphur dioxide Aceticacid Amyl alcohol (fusely) Oaky/woody

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Smoky/Phenolic Associated with astringent fruits Burnt/Acrid/Rubbery Dimethylsulphide/Cabbage-like/Cookedvegetable Yeasty Marmite/Soysauce Damp cardboard/Sawdust Musty Straw Cheesy Other characteristics Off aroma not covered above

Table 2 Chemical/physical measurements relating to sensory aspects of foods and beverages Measurement 1. Lighttransmittance/reflectance visual spectra tristimulus values

2.

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ultra violet near infra-red Sizeand shape grading visual analysis Gas chromatography volatile components Liquid chromatography non-volatile components Simplechemical/physical measurements pH, specific gravity, titratable acidity

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density, fibre weight, alcohol insoluble solids, moisture

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Food Quality attd Preference (1988) 1 (1)

28

Williams, Rogers and Collins

tion techniques that attempt to reduce the number of analytical variables used in a particular exercise also have to be treated carefully. Just as the sensory information should be made as precise as possible before attempting to determine its origin, so should the chemical/physical data. Unlike the sensory data, where one has to rationalise the response, in many cases there is no ambiguity about the measurement being taken, e.g. pH, tristimulus values or in the majority of compounds separated by chromatography. In other cases, however, particularly when dealing with trace components, one cannot always be certain that measurements that appear to relate to a particular compound do in fact do so; in the case of gas chromatographic data retention times may shift, peaks may merge and overlap, and different components may have similar retention times in different products. The routine use of confirmatory techniques, such as mass spectroscopy, would appear to be the only way of overcoming these problems.

Methods for relating sensory to chemical/physical information Several approaches are available for relating sensory to chemical/physical data (Williams et al. 1984). Some are mathematical in nature, and use complex multivariate procedures (e.g. Martens & van den Burg 1985), while others are not and involve, for example, the evaluation of the flavour response to separated compounds or fractions, or the use of threshold measurements and odour unit concepts (Williams 1978; Acree & Cottreil 1985; Christoph & Drawert 1985; Maarse & van den Berg in press). Whilst each approach has its merits, a complete understanding of chemical/ physical/sensory relationships can only be achieved by integrating information from all sources. Mathematical approaches tackle the problem in its entirety and attempt to isolate groups of compounds which give rise to a particular response. However, unless it is possible to recreate this response from information on individual components (e.g. odour descriptions and threshold information), one cannot claim to have a thorough understanding of the origin of sensory characteristics. A number of the mathematical techniques available for relating sensory and chemical/physical information are given in Table 3. Several of these methods, namely multiple regression (Draper & Smith 1981), canonical correlation (Hotelling 1936), redundancy analysis (van den Wollenberg 1977; Tyler 1982) principal compoFood Quality and Preference (1988) 1 (1)

nent regression (Jolliffe 1986) and partial least squares analysis (Wold et al. 1983a, 1983b), will be described briefly here, these being some of the more commonly used techniques for relating data sets of this nature (e.g. Piggott 1986; Martens et al. 1983; Fornell & Bookstein 1982). Only the concepts behinds the methods will be addressed; full algebraic details can be found in the references cited above. Table 3 Mathematical approaches for relating chemical/physical and sensory data

1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

Linear regression and correlation. Non-linear regression using specific models. Multiple regression using raw or transformed data. Canonical variate analysis on defined groups. Correlation and regression using principal axes following principal component or canonical variate analyses. Canonical correlation and regression. Partial least squares regression. Procrustes matching. Redundancy modelling. LISREL, maximum likelihood modelling.

With the exception of multiple regression they all aim to identify underlying factors or components within the data sets. It is assumed that the inter-relationship between two sets of variates may be conveyed by means of these factors. Canonical correlation identifies pairs of related factors (canonical variates), each linear combinations of the respective chemical and sensory variates. In contrast, principal component regression, partial least squares and redundancy analysis identify a single set of factors, linear combinations of the chemical/physical variables, which are related to the sensory data by means of a regression equation. In order that one may hope to identify meaningful relationships there are a number of criteria to consider: (a) the correlation between a chosen factor and the response variables; (b) the ability of the factors to explain the sensory responses, i.e. to minimise the error of prediction of the sensory variates; (c) the ability of the factors to summarise the chemical/physical information. In order to understand each of these aspects fully it is useful to resort to vector space concepts and geometric representations of the data. As described previously when discussing the sensory data (Fig. 1),

data spaces may be viewed as a sample space. Here the reference axes correspond to the sensory attributes or chemicaV physical parameters measured, and the samples are represented as points within the space. Alternatively, the data may be viewed as a variable space. In this case the orthogonal reference axes correspond to the samples and the attributes or variables are represented as vectors (lines) through the space (Fig. 4). Since, with this representation, the reference axes (samples) are common to both the chemical/physical and sensory spaces the vectors from each data source are contained in a common multidimensional space. The derived factors (also represented as vectors), used for modelling, are linear combinations of the predictor (chemical/physical) or sensory variables, and as such lie in the subspaces spanned by these variables.

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Geometrically the correlation between a factor and a sensory attribute, or between two factors, corresponds to the cosine of the angle (0 in Fig. 5) between the vectors representing them. On the other hand, the ability of the factors to predict the sensory information is given by the sum of squared distances between the true sensory variates and the estimates after orthogonal projection on to the subspace spanned by the chosen factors (S to S' in Fig. 6. For diagrammatic clarity only a single sensory variate is indicated). Similarly, the extent to which the factors summarise the information provided by the analytical variates is given by the sum of squared distances obtained when each of these analytical variables is projected on to the space spanned by the chosen factor or factors (Fig. 7). In practice those factors which satisfy a criterion of minimal error of prediction, (b) above, will not be the same factors as those which provide the best summary of the analytical space (i.e. account for the most variation in the analytical data), (c) above.

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The criteria by which the factors are chosen for each of these methods are as follows: Canonical correlation - This optimises criterion (a), extracting pairs of factors which show maximum correlation (minimum angle). No consideration is given to either predictability of the amount of variation explained in the two component data sets. Principal c o m p o n e n t regression - The prin-

29

cipal component factors are chosen on the basis of their ability to summarise the information provided by the analytical variates. That is, they are chosen to minimise the sum of squared distances marked A to A ' (Fig. 7), over all of the variates. Thus they are chosen to satisfy condition (c) above. R e d u n d a n c y analysis - In contrast, the redundancy factors are chosen to optimise the predictive ability of the model (criterion (b)). They are chosen to minimise

Partial least squares analysis - This attempts to combine both of these aspects, (b) and (c), by.taking into account both the ability of the factors to summarise the analytical information and their ability to predict the sensory variates. This is achieved, not by minimising a sum of squares or maximising a correlation, but by optimising a function of the covariance between the two sets of variables. When considering the various methods as possible means of deriving relationships between sensory and analytical data it is important to be aware, not only of the inherent differences between the techniques, but also of the implications of such differences. One of the limitations of the principal component approach arises from the fact that the factors are chosen in ignorance of the distribution and location of the sensory variables within the space. Although the variance of the estimated regression coefficients will be minimal (Greenberg 1975) there is no guarantee that the estimates obtained will be good ones. The correlations may be poor, with large residual sums of squares being observed. While it has been proposed by several authors (including Lott 1973, and Hill et al. 1977) that the principal components be retained on the basis of their correlation with the sensory response, rather than their ability to summarise the analytical data, this is not as simple a task as it may seem. When the number of sensory variables exceeds one, and different principal components show 'high' correlations with different sensory variates, a problem arises in deciding which components should be retained. While the redundancy analysis and multiple regression solutions are guaranteed to provide the smallest prediction errors, they exhibit other undesirable features. The stability of the resultant regression estimates, determined using any of these methods, is influenced by the distribution and positioning of the chemical/physical variates within the space. In particular they are highly influenced by the lower, less important principal dimensions. Since neither redundancy analysis nor multiple regression consider the relative positioning of these chemical/physical variates within the predictor subspace, the projected response variables (and hence factors) could in principle lie in the subspace associated with random noise in the data, i.e. they Food Quality and Preference (1988) 1 (1)

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Williams,Rogers and Collins

could lie in the subspace spanned by the minor principal axes. Although it may be argued that this would simply indicate that the choice of predictors was a poor one, the instability and large variance of the regression coefficients when the model is not constrained to more important chemical/physical dimensions cannot be ignored (Silvey 1969; Beisley et al. 1980). Of course, since canonical correlation considers neither criterion (b) nor criterion (c) all of these points apply to this method also. One further, not uncommon, feature when dealing with data of this nature is for the number of variates to exceed the number of samples assessed, e.g. when relating sensory information to gas chromatographic data. The dimensionality of the variable space is determined by the number of samples (n). Thus when the vectors representing p analytical and q sensory variables are placed in it, we have an n-dimensional space containing p + q vectors. In any practical application, if p > n, these p predictor vectors will span the entire ndimensional space. Hence the q sensory responses will be expressible solely and completely in terms of the p vectors. Thus in this case the projection of the sensory variates coincide with the variates themselves. This situation presents problems for the methods of redundancy analysis, multiple regression, and canonical correlation. At most n linearly independent vectors span an n-dimensional space. Since we have p such vectors, with p > n, it follows that they must be linearly dependent (collinear). When collinearity occurs the last (p - n - 1) principal dimensions through the chemical/physical space define these linear dependences. They do not explain

any of the variation in the chemical/ physical data. As the solutions are highly influenced by these lower dimensions and are not, with these methods, constrained to the more important axes, highly unstable, ill-defined solutions result. Collinearity amongst the predictors will always occur when n < p and it may occur when n > p. Also, when the space spanned by the sensory variates is completely contained in the analytical space, it is possible to find multiple pairs of perfectly correlated canonical factors (i,e. with a correlation of one). When there are several such pairs, the factors can be neither uniquely positioned nor defined. While the partial least squares approach is not necessarily the ideal method, there never being a guarantee that one will be able to readily interpret the results in terms of current knowledge of the products, it does attempt to circumvent and overcome some of the limitations of the other approaches. By considering the distribution of the analytical variables and giving a greater importance, when choosing the factors, to those dimensions which explain more variation in the physical/chemical data, the method attempts to avoid the problems of instability associated with techniques that do not constrain the subspace in this way. Similarly, by simultaneously addressing the question of the predictive ability of the model the problem of large prediction errors, which may be encountered with the principal component approach, is also to some extent avoided. Of course, the solution obtained will neither show the same predictive ability as the redundancy or conventional regression solutions nor will it summarise as much of the chemical/physical data as the principal component model. It is rather a comprom-

ise between the two. Each of these techniques was u.sed to describe the relationship between the sensory aroma of the Beaujolais Nouveau wines discussed earlier to gas chromatography (GC) results. The data consist of the standardised mean logged peak areas of 30 volatile compounds identified using direct injection of samples into a GC column. Each peak corresponds to different compounds in the sample, with the peak area indicating the amount of the compound present (Eti6vant et al., in preparation). The sensory data were first rationalised by Procrustes matching, and for the purposes of this illustrative example, only the first consensus dimension was retained for modelling. The results presented in Table 4 relate to the modelling of these data using principal component regression, partial least squares regression and conventional multiple regression (equivalent to redundancy analysis here). In the case of the principal component and partial least squares regression, only a single dimensional subspace was used. The multiple regression solution provides a perfect fit to the data, but the information it contains is not necessarily useful, and the solution, in this case, is highly unstable. The first principal component through the analytical subspace accounted for 39% of the variation in the GC data, but exhibited a negligible correlation with the sensory consensus variable. The partial least squares factor, on the other hand, although accounting for slightly less variance (25%) in the analytical data, showed a reasonable correlation with the sensory variable (53% of the variation in the sensory response explained by the model). Inclusion of the second principal

Table 4 Relationships between chemical and sensory data from Beaujolais Nouveau wines, as identified using multiple regression, principal component regression and partial least squares regression First sensory consensus dimension following Procrustes analysis (major attributes identified)

Synthetic cherryade contrasted with vegetative

Main GC peaks identified using: Multiple regression

Principal component regression (first dimension only) % var. in chemical data explained by factor = 39 ,

Partial least squares regression (first dimension only) % var. in chemical data explained by factor = 25

Major peaks identified (nos)

Vat. in sensory data explained

Major peaks identified (nos)

Var. in sensory data explained

Major peaks identified (nos)

Var. in sensory data explained

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Relating chemical/physical and sensory data in food acceptance studies

component factor (accounting for 19% of the variation in the G C data) did not improve the predictive ability of the model. In the case of the partial least squares model the inclusion of a second dimension increased the percentage variation accounted for in the analytical data to 48% and the resultant regression equation explained 82% of the variation in the sensory response.

Conclusion When relating sensory and chemical/ physical data rationalising sensory data prior to attempting to identify relationships improves the chance of getting meaningful results. The more commonly used approaches used for deriving such relationships have their limitations. Partial least squares analysis, because of its ability to take into account variation in the analytical data as well as the correlation with the sensory data, has the potential to produce the most meaningful information.

Acknowledgements This work was part of a collaborative project between the University of Bath and Long Ashton Research Station. C A R would like to thank the Sir Keith Showering Memorial Trust for financial support, and Long Ashton Research Station for the provision of facilities.

References (1985) C h e m i c a l indices of wine quality. In Alcoholic Beverages, (eds G G Birch & M G Lindley), Elsevier Applied Science: London, New York ARNOLD, G M & WILLIAMS A A (1986) The use of generalised Procrustes techniques in sensory analysis. In Statistical Procedures in Food Research (ed. J R Piggot), pp. 233-54. Elsevier Applied Science: London, New York BELSLEY, D A, KUH, E & WELSCH, a E (1980) Regression Diagnostics, John Wiley: New York CHRISTOPH, N & DRAWERT F (1985) Olfactory thresholds of odour stimuli determined by gas chromatography sniffing technique: structure activity relationships. In Topics in Flavour Research (eds R G Berger, S Nitz & P Schreier) H. Eichhorn: MarzlingHangenham, West Germany DRAPER, N R & SMITH, H (1981) Applied Regression Analysis, 2nd edn. John Wiley: New York ETII~VANT, P X & WILLIAMS, A A (1985) Influence ACREE, T E & Co'VrRELL, H E

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of storage on some sensory and physicosensory significance of chemical data in flachemical characteristics of Beaujolais vour research, Parts I-III, International FIRNouveau wines. In Current Technical Deyours and Food Additives, 9, 80-5, 131-2, velopments. Proceedings of the 9th Wine 171-5 Subject Day (ed. F W Beech). Long Ashton WrLLIAMS,A A (1983a) Defining sensory quality Research Station: Bristol in foods and beverages, Chemistry and IndusFORNELL, C & BOOKSTEIN, F L (1982) Two try, 740-5 statistical equation models: LISREL and PLS WILLIAMS, A A (1983b) Measuring the competiapplied to consumer exit voice theory, Jourtiveness of wine, in tartrates and concentrates. nal of Market Research, 19,440-52 In Proceedings of the 8th Wine Subject Day GOWER, ,i C (1975) Generalised Procrustes analy(ed. F W Beech) pp. 3-12. Long Ashton sis, Physcometrika, 40, 33-51 Research Station: Bristol GREENBURG, E (1975) Minimum variance prop- WILLIAMS, A A (1985) The use of perceptual erties of principal component regression, space approaches for determining the influJournal of the American Statistical Associaence of intrinsic and extrinsic factors on food tion, 70,194-7 choice. In Consumer Behaviour Research and HILL, R C, FOMBY, T B & JOHNSON, S R (1977) Marketing of Agricultural Products. ProceedComponent selection norms for principal ings of tire Agro Food Workshop Organized component regression, Communications in by the Commission of the European ComStatistics: Theory and Methods, A6,309-34 munities (ed. J E R Frijters) pp. 29--37. HOTELLING,H (1936) Relations between two sets National Council for Agricultural Research: of variables, Biometrika, 28, 321-77 The Hague JOLLIFFE, I T (1986) Principal Component Analy- WILLIAMS, A A (1986) Some new ideas for sis. Springer-Verlag: New York measuring customer attitudes to wines. In Lorr, w F (1973) The optimal set of principal Quality Assurance in the Wine hldustry. Procomponent restrictions on a least squares ceedings of the lOth Wine Subject Day. pp. regression, Communications in Statistics, 2, 85-94. Institute of Food Research: Reading 449--64 Laboratory MAARSE, H & VAN DEN BERG, F (in press) Current WILLIAMS, A A (in press) Procedures and probissues in flavour research. In Distilled Beverlems in optimizing sensory and attitudinal age Flavour: Recent Developments (ed. J R characteristics in foods and beverages. In Piggott). Ellis Horwood: Chichester Proceedings of tire International Symposium MARTENS,M (ed.) (1987) Data-approximation by on Food Acceptance, University of Reading, PLS methods, Report No. 800. Norwegian September 1987 Computer Centre WILLIAMS, A A & ARNOLD, G M (1984) A new MARTENS, M & MARTENS, H (1986) Partial least approach to the sensory analysis of foods and squares regression. In Statistical Procedures hi beverages. In Progress in Flavour Research, Food Research (ed. J R Piggott) pp. 293-359. 1984. Proceedings of the 4th Weurman Flavour Elsevier Applied Science: London, New York Research Symposium (ed. J Adda) pp. 35-50. MARTENS, M , MARTENS, H & WOLD, S (1983) Elsevier: Amsterdam Preference of cauliflower related to sensory WILLIAMS, A A, ROGERS, C A & NOBLE, A C (1984) descriptive variables by partial least squares Characteristics of flavour in alcoholic bever(PLS) regression. Journal of the Science of ages. In Fluvour Research of Alcoholic BeverFood and Agriculture, 34,715-24 ages, Instrumental and Sensory Analysis, (eds MARTENS, M & VAN DEN BURG, E (1985) Relating L Nykanen & P Lehtonen)0 pp. 235-53. sensory and instrumental data from vegetFoundation for Biotechnical and Industrial ables using different multivariate techniques. Fermentation Research: Helsinki In Progress in Flavour Research, 1984. Pro- WOLD, S, ALBANO, C, DUNN, W 'i Ill, EDLUND, U, ceedings of the 4th Weurman Flavour Research ESBENSEN, K, GELADI, P, HELLBERG, S, Symposium (ed. J Adda) Elsevier: AmsterJOHANSSON, E, LINDBERG, W & S.IOSTROM, M dam (1983a) Multivariate data analysis in chemisMCEWAN, J & THOMSON, D M H (1988) A try. In Chemometrics and Mathematics in behavioural interpretaton of food acceptabilStatistics and Chemistry (ed. B Kawalski), pp. ity, Food Quality and Preference, 1,3-9 17-96. Nato ASI Series PIGGO'r-r, ,i R (1986) Statistical Procedures in WOLD, S, ALBANO, C, DUNN, W 'i I l l , ESBENSEN, K, Food Research. Elsevier Applied Science: HELLBERG, S, 'IOHANSSON, E & S'IOSTROM, M London, New York (1983b) Pattern recognition in finding and SILVEY, S D ( 1 9 6 9 ) Multicollinearity and impreusing regularities in multivariate data. In cise estimation, Journal of the Royal Statistical Food Research and Data Analysis (eds H Society B, 31,539-52 Martens & H Russwurm), pp. 147-88. ApTYLER, D E (1982) On the optimality of the plied Science: London simultaneous redundancy transformations, VAN DEN WOLLENBERG,A L (1977) Redundancy Psychometrika, 47, 77-86 analysis, an alternative to canonical correlaWILLIAMS, A A (1978) Interpretation of the tion analysis, Psychometrika, 42,207-19

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