[This paper was read  at the Conference on the investigation of social space, Cologne, October 7-9 1998; the conference was organized by J. Blasius and H. Rouanet with the cooperation of Bourdieu,  and held with  his participation. The paper appeared in Bulletin de Méthodologie Sociologique, 2000, 65, 5-15.]

Résumé

Ce texte étudie en détail l'usage de l'analyse des correspondances dans La Distinction (1976/79) de Bourdieu, en ayant en vue les sociologues qui souhaitent analyser leurs données selon des méthodes en harmonie avec celles de Bourdieu. Pour Bourdieu, l'analyse des correspondances n'est pas un outil parmi d'autres commode pour visualiser les données, mais un instrument unique éminemment apte à découvrir les deux espaces apparentés des individus et des propriétés. Un examen attentif de La Distinction révèle un usage réfléchi et créatif de l'analyse des correspondances, appliquée à des tableaux Individus x Propriétés, avec ses principales aides à l'interprétation. Les conclusions majeures de cette "leçon'' demeurent valides aujourd'hui, elles sont applicables à tout tableau Individus  Propriétés, analysé par l'analyse des correspondances ou plus particulièrement par l'analyse des correspondances multiples. Dans l'analyse des questionnaires, faire des analyses de correspondances ne suffit pas pour faire des analyses "à la Bourdieu''. L'espace fondamental doit être construit à partir d'un ensemble de variables pertinentes suffisamment ample pour permettre le plein déploiement multidimensionnel des individus.
Mots-clefs. La Distinction de Bourdieu. Analyse Géométrique des Données. Tableaux Individus x  Propriétés, Analyse des Correspondances. Nuage des individus, représentation simultanée.

Summary

This paper investigates the use of Correspondence Analysis (CA) in Bourdieu's La Distinction (1976/79), having in mind the sociologists who wish to analyze their data in a way in harmony with that of Bourdieu. For Bourdieu, CA is not simply a handy tool among others for visualizing data, but a unique instrument apt to uncover the two related spaces of individuals and of properties. A careful reading of La Distinction reveals a thoughtful and creative use of CA, applied to Individuals x Properties tables, with its main aids to interpretation. The major conclusions from this "lesson'' remain valid today and generally apply to Individuals x  Properties tables whether analyzed by CA or more specifically by Multiple Correspondence Analysis (MCA). In the analysis of questionnaires, doing correspondence analyses is not enough to do "analyses à la Bourdieu''. The fundamental space must be constructed from a set of relevant variables ample enough to allow the full multidimensional display of individuals.
Key-words. Bourdieu's La Distinction. Geometric Data Analysis, Individuals x   Properties tables, Correspondence Analysis, Cloud of individuals, Simultaneous Representation.

Introduction: the paradigm of La Distinction

Correspondence Analysis (CA) has been used in the work of Pierre Bourdieu, at least since his article "Anatomie du Goût'' (Bourdieu & Saint-Martin, 1976), with the analysis of the epoch-making questionnaire on Lifestyle taken up later in the book La Distinction (Bourdieu, 1979). In this type of analysis - henceforth referred to as "the paradigm of La Distinction ''- the basic data set is an Individuals x Properties table ; and the basic output consists of two clouds of points: the cloud of individuals and the cloud of properties . The interpretation is based on a joint study of the two clouds. The paradigm of La Distinction has been continuously used by Bourdieu and his coworkers in the analyses of questionnaires to construct and investigate social spaces. In recent issues of Actes de la recherche , we find Sapiro (1996) (a study on the French writers during the German occupation), and Lebaron (1997) (a study of economists). In our presentation of the Geometric Analysis of Questionnaires, we will especially have in mind the sociologists of the international community who wish to analyze and interpret their data in a way in harmony with that of Bourdieu. This has motivated us to comment on the privileged link between Bourdieu's construction of social space and Geometric Data Analysis, using La Distinction as a leading thread. It should be noted that in "Anatomie du Goût'' (1976), as well as in La Distinction , the technique referred to by Bourdieu to analyze Individuals x Properties tables was "Correspondence Analysis''. Around that time, for such tables, the method known as Multiple Correspondence Analysis (MCA) was becoming a standard for Analyzing questionnaires. Since the late seventies, most analyses conducted by Bourdieu and his colleagues have systematically been Multiple Correspondence Analyses. The methodological comments made in the present paper are by and large applicable to the paradigm Individuals x   Properties tables, beyond the strict properties of MCA

The Lesson of La Distinction

Elective affinities [Wahlverwandtschaften] Before analyzing the privileged link between Bourdieu's sociological thinking and Geometric Data Analysis, let us state right away that if Bourdieu refrained from using more conventional statistical techniques, such as regression, it is certainly not out of ignorance. Here is what we read in the Foreword of the German edition of Le Métier de Sociologue :" If I had sought to explain which are the factors that determine [bestimmen] the achievements of pupils in various schools, I would have used multiple regression analysis... provided that , etc...''. The provisos were not fulfilled, so Bourdieu did not use regression analysis. In numerous passages of La Distinction , Bourdieu has explained the reasons for this reluctance. Procedures like regression are too much in line with the sociology of variables -- a trend to which Bourdieu strongly objects.

The particular relations between a dependent variable (political opinion) and so-called independent variables such as sex, age and religion, tend to dissimulate the complete system of relations that make up the true principle of the force and form specific to the effects recorded in such and such particular correlation ( La Distinction , p. 103).
One could multiply similar quotations (e.g. p.11, 113, 117...)

From spatial vision of society to spatial representation of data
The spatial vision of society. In our opinion, in order to realize how strong the link between Bourdieu's thinking and Geometric Data Analysis is - so strong indeed that it amounts to genuine elective affinities (Wahlverwandtschaften) - we must start with the "spatial vision'' of society (Raumvorstellung) which is a constant in Bourdieu's thinking. This spatial vision leads him to uncover and emphasize the material support of social relations in physical space surrounding us. The city map of nineteenth century Paris is the guide for Bourdieu's analysis of Flaubert's Education Sentimentale , just as the districts ("Grands ensembles des banlieues'') where the poor live today is the guide of La Misère du Monde . Incidentally, it is in La Misère du Monde that we find perhaps the most thorough exposition of Bourdieu's spatial vision in a chapter entitled "Effets de Lieu'' (Effects of location). For Bourdieu, social relations and oppositions are first and foremost spatial relations and oppositions.
The spatial representation of data. It is this spatial vision of Bourdieu, we think, that in turn has led him, in order to analyze surveys and questionnaires, to favor a method in which the differences, deviations, distinctive traits among individuals are cast in "spatial'' terms [Raumdarstellung], namely the geometric method of Correspondence Analysis. For Bourdieu, Correspondence Analysis (CA) is not simply a handy tool among others for "visualizing data''. Bourdieu clearly perceived that, starting from complex statistical relations, CA was going to be a unique instrument to construct and study two geometric spaces: . on the one hand, a space (analogous to physical space) in which individuals are located -- a space that Bourdieu calls (most appropriately) the "space of individuals''; . on the other hand, and in simultaneous representation with the space of individuals, another space that displays the complexity of statistical relations expressing social relations -- and which Bourdieu calls "the space of properties''.

"I use Correspondence Analysis very much, because I think that it is essentially a relational procedure whose philosophy fully expresses what in my view constitutes social reality. It is a procedure that 'thinks' in relations, as I try to do it with the concept of field.'' (Foreword of the German edition of Le Métier de Sociologue , 1991).

Going over La Distinction
Let us now comment on this geometric approach of Bourdieu, taking La Distinction as a leading thread. The frame-model of La Distinction. In the section of La Distinction entitled "A Three-Dimensional Space'' (La Distinction, p.128), Bourdieu describes the knowledge relevant to Lifestyle, displayed in the famous synoptic diagram of La Distinction . See Diagram 1 [p.140-141]. What we call the frame-model of La Distinction is the mathematical (multidimensional geometric) model underlying this diagram. An individual is characterized by three fundamental dimensions: Economic, Cultural and Social Capital [p.138]; and the overall cloud of individuals (upper, middle and popular classes put together) is such that its two principal axes are the Volume of Capital and the Structure of Capital. Aids to interpretation. A careful reading of La Distinction shows that the main aids to interpretation devised in the early seventies for Geometric Data Analysis were extensively and judiciously used by Bourdieu, as reflected firstly in the inertias of principal axes (expressed in percentages, as indicated p.295), secondly in the contributions of points to axes (see footnote 4, p.295).
Simultaneous representation. In La Distinction , two correspondence analyses performed on the survey about lifestyle are presented: one for the upper class and one for the middle class. The simultaneous representation is constantly used to substantiate the interpretation of these analyses. For instance, Diagram 2 [p. 296] for the upper class is the simultaneous representation of two graphs: Graph 11 of Properties and Graph 12 of individuals of different social class fractions (We will discuss later the graphical representations of those social fractions). In the book, the two sorts of points appear in different colors (black vs red); in the "Urtext'' of 1976, the simultaneous representation was materialized by superimposed transparent papers!
Supplementary questions. In the Correspondence Analyses of La Distinction , the status variables (age, father's profession, education level, income) are set out (with the exception of social fractions) as supplementary elements , that is, they do not participate to the construction of the social space, but they are represented as points in the space of properties. This was done, Bourdieu points out, in order to "give its full strength'' to the demonstration that the differences in lifestyle are interpretable in terms of status. This means that Bourdieu was deliberately making an explanatory use of CA (going against the misbelief that CA is a "merely exploratory'' procedure).
Specific analyses. Guided by the idea of homology between classes, Bourdieu compares the upper class and the middle class homologous subclouds. See Diagram 3 [p. 300 and 394], in which, for instance, the profiles of education levels for axes 1 and 3 are drawn for the two classes.
Structuring factors in the space of individuals. Finally, in La Distinction , Bourdieu makes use of what we now call structuring factors in the space of individuals. Let us take again Diagram 2 for the upper class. For each social fraction, a geometric contour indicates a zone within which most of the individuals belonging to this fraction are concentrated. Thus, on the left of the diagram, a slanted rectangle indicates the zone of university professors ("professeurs supérieurs'') and art producers; in the central area of the diagram, there is a rectangle for liberal professions ("professions libérales''); on the right, there is a triangle for the heads of business firms ("patrons du commerce''), etc. For executives of the public and private sectors ("cadres du public'' and "cadres du privé''), no contours have been drawn, because, as Bourdieu tells us in a footnote [p.297], the individuals are scattered throughout the whole plane. It is patent that such contours, which sketch the dispersions in amount and in direction (shape) of the subclouds of individuals for the various social fractions, are stylized representations (presumably motivated by typographical convenience) of these subclouds (Such stylized representations of the various subclouds of individuals could be conveniently provided by concentration ellipses automatically drawn by graphical software). If we scrutinize the text of La Distinction , we can discover the intuition that led Bourdieu to consider the social fractions as a structuring factor of individuals rather than a set of supplementary modalities. Take for instance, for the upper class, the three fractions "professions libérales'', "cadres du public'' and "cadres du privé''. Apparently, the mean points of these three clouds are close to the center of the diagram, and close to one another. Therefore, if social fractions had been put as supplementary elements, the three fractions would have been merely represented (in the space of properties) by three points around the center of the diagram and close to one another, and the discrepancies in dispersion (in the space of individuals) among the subclouds would have been missed. Thus conceptualizing the social fractions as a structuring factor of individuals and sketching the shape of the corresponding subclouds gives -- as we will say in turn -- all its subtlety to the demonstration that the differences in lifestyle are interpretable in terms of social fractions.

The individuals, always the individuals! Benzécri wrote somewhere: "All in all, doing a Correspondence Analysis is nothing more than diagonalizing a matrix. The point is just to pick up the right matrix to diagonalize''. The way in which Bourdieu has constantly used CA always consists in typically taking, as a basic matrix, an Individuals x  Modalities table, where the set of modalities covers the full set of relevant questions, and therefore is typically ample enough to entail an adequate "multidimensional display'' for the two ensuing basic clouds of individuals and of modalities (This closely concurs with the famous Benzécri requirement of "exhaustivity'': see e.g., Benzécri, 1992, p.383). From the basic cloud of individuals, which carries the whole of information, derived clouds can always be obtained, such as the cloud of the mean points of social fractions. Taking on the contrary aggregated data as the basic input for CA goes against the very concept of social space in Bourdieu's sense and simply amounts to using CA to do sociology of variables. The interest of representing the individuals themselves is obvious enough when the individuals are known persons, such as, in Homo Academicus , where the individuals are university professors. When the individuals are "anonymous'', as in many surveys, the interest of representing them may seem less obvious. Still, as the reading of La Distinction suggests, whenever we deal with an important structuring factor (such as social fractions), it is strongly recommended not to be confined to mean points, but to assess the variability among individuals within the factor levels (i.e. social fractions), that is, the subclouds themselves should be represented, or at least informative summaries sketching the amount and the principal directions of dispersion. As for Bourdieu's concept of Habitus -- a permanent disposition attached to individuals -- it establishes the link between the positions of individuals in the social space and their various observable manifestations (tastes, declarations, etc.). Now, even though positions in the social space may not determine entirely those manifestations, they surely control their probabilities (their facilities , as Laplace would have said). If we understand Bourdieu correctly, habitus, like probability, is a two-fold concept, both individual and collective. Following this line of thought might lead, in carefully chosen situations, to use the individual probabilities produced by regression analyses (esp. logistic regression) to investigate habitus within the geometric framework

Conclusion

As early as 1976, with the survey on lifestyle taken up later in La Distinction in 1979, Bourdieu made a thoughtful and creative use of Correspondence Analysis. The major conclusions from this "lesson'' remain valid today. 1. In the analysis of questionnaires, doing correspondence analyses is not enough to do "analyses à la Bourdieu''. The fundamental social space must be constructed from an extensive set of relevant variables and ample enough to allow the full multidimensional display of individuals. 2. Using Correspondence Analysis does not preclude other statistical techniques (such as regression so much in favor today); yet to keep in line with Bourdieu's approach of social space, those techniques should be not just juxtaposed but integrated into the geometric representation, which must remain at the heart of interpretation. 3. On a practical level, extensive geometric data analyses can be carried out today more easily than ever, and the improvement of graphical displays can make the detailed exploration of clouds especially fruitful. By continuing to plead for a creative use of Geometric Data Analysis taking into account the advances of statistical art - as described e.g. in Le Roux, Rouanet (1998) - we are also pleading for a construction and investigation of the social space fulfilling Bourdieu's wish, that is, uniting the construction of the object and the instruments necessary to turn a research program into a scientific work.

REFERENCES

Benzécri J.P. et al. (1973) - L'Analyse des Données. Vol I: La Taxinomie. Vol II. L'Analyse des Correspondances. Paris: Dunod.
Benzécri J.P. (1992) - Correspondence Analysis Handbook. New York: Dekker [adapted from J.P. & F. Benzécri (1984), Pratique de l'Analyse des Données: Analyse des Correspondances & Classification, exposé élémentaire , Paris, Dunod].
Bourdieu P. & Saint-Martin M. (1976). "Anatomie du goût''. Actes de la recherche en sciences sociales , 5, 1-110.
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Le Roux B., Rouanet H. (1998). "Interpreting Axes in Multiple Correspondence Analysis: Method of the Contributions of Points and Deviations'', pp. 197-220, in J. Blasius & M. Greenacre (Eds): Visualization of Categorical Data . London: Academic Press.
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COMMENT  (October 2005)

As indicated above, this paper was read at the 1998 Cologne conference held in homage to Bourdieu with his participation.
Its aim was twofold : 1) retrospective : clarify the use by Bourdieu of Correspondence Analysis since 1976, especially in La Distinction. 2) prospective: point recent advances in Geometric Data Analysis. The prospective part was firstly reflected by Bourdieu himself (1999) in his study of the field of publishers; then, after the mourning period, it is now carried out by Bourdieu's followers. See e.g. Hjellbrekke, Le Roux, Korsnes, Lebaron, Rosenlund, Rouanet : The Norwegian field of power, European Societies, 9(2), p.245-273 (2007).