An invitation to quantify Bourdieu in educational research

Pierre Bourdieu is a philosopher by training and a sociologist by choice. His theory and practice have far-reaching influence across a wide range of disciplinary fields such as economy, law, religion, sport, culture, language, art and literacy, science and political science and, of course, education. Intellectual engagements with Bourdieu include the celebration and consecration of his sociological armoury, the application and extension of his sociological tools, and the perennial debates around the question of whether or not his sociology falls prey to determinism and methodological nationalism. These engagements make Bourdieu one of the world’s most cited and contested social scientists.

As a theorist of practice, Bourdieu argues against the ‘fictitious antinomies’ between theoreticism and empiricism. For this reason, Bourdieu is one of the most empirical theorists among the ‘academic celebrities’ of the last century. His empirical work largely unfolded in the national context of Algeria at the time of the war of independence and of France at the time of massification of higher education and the rise of market ideology and neoliberalism. Bourdieu’s empirical forays generate theories that enable the explanation and analysis of not only structural configurations of social spaces but also individual and collective internalisation and externalisation of social orders and structural forces. Such theorising, at the philosophical level, constructs ‘third-level knowledge’ that transcends classificatory thinking and dissolves a plethora of ‘meaningless oppositions’ between objectivism and subjectivism, between statistical evidence and ethnographic narrative. In this vein, Bourdieu’s sociology is congruent with methodological polytheism.

In their well-received and much-needed anthology Bourdieu and Data Analysis: Methodological Principles and Practice(2014), Michael Grenfell and Frédéric Lebaron put together a collection of investigations that qualitatively and quantitatively wade into complex and difficult issues of language, culture, economy, politics, and education. Their volume powerfully ventures into and capitalises on Bourdieu’s methodological pluralism. In educational research, however, there is a striking underrepresentation of Bourdieusian publications that incorporate a quantitative component. The problematic dearth of quantitative Bourdieusian work came to the attention of Karen Robson and Chris Sanders, who edited a volume in 2009 on Quantifying Theory: Pierre Bourdieu. Of all the 16 chapters, there are only three that focus on education. The scarcity of quantitative Bourdieusian scholarship in educational research persists. For example, in the British Journal of Sociology of Education, where the famed sociologist is featured most strongly among all educational journals, readers are only presented with a dire volume of quantitative Bourdieusian research.

It is a disappointing fact that there is a lack of appreciation and presentation of quantitative Bourdieusian work in the scholarly community of educational research. Reasons behind this disappointment abound. First, the dominance of qualitative Bourdieusian educational research can become a doxic belief. When qualitative engagement with Bourdieu is prominent, it becomes so legitimate that it does not warrant any justification or requires any contestation. When the doxaof using Bourdieu qualitatively remains unquestioned and unquestionable, its symbolic power is reproduced and reinforced, which can further marginalise the position of quantitative Bourdieusian educational research. Second and relatedly, certain Bourdieusian concepts, habitus, in particular, are nebulous and pose a methodological challenge to quantify. This can also become a doxic belief that concepts such as habitus are not quantifiable. This very doxadiscourages or even rules out the methodological venture into the quantitative Bourdieusian domain. Any endeavour to quantify Bourdieu may be seen as a methodological fallacy and an epistemological heresy. Next, many Bourdieusian educational colleagues have not been offered the opportunity for training in quantitative research. Inadequate quantitative literacy may translate into a disposition of discomfort with, diffidence in, and sometimes defiance of quantifying Bourdieu. Finally, Bourdieu himself barely explicitly reports on his analytical procedure. His way of reporting violates the convention of the American quantitative, positivist school that requires detailed validation of quantification. Such violation offends quantitative traditions and inhibits a clear understanding of what exactly Bourdieu has done statistically.

Bourdieu’s breach, consciously or unconsciously, of the conventions of reporting quantitative research is problematic because it creates such a pain for the reader to make sense of Bourdieu statistically. More problematic, however, are the doxic belief in qualitative Bourdieusian educational research, the doxic disbelief in quantitative Bourdieusian educational research, and the dispositional inferiority in quantifying Bourdieu, all of which are blasphemous against Bourdieu’s methodological polytheism. Here I want to make my point of departure squarely clear: It is by no means my intention to claim that Bourdieusian educational research is qualitatively too thick; rather, it is quantitatively too thin. In response to this problem, I invite my education fellows to engage (more) with quantitative Bourdieusian investigations and more importantly, I propose to put Bourdieu to work quantitatively. To this end, I draw the readers’ attention to a series of statistical models, namely multiple correspondence analysis, cluster analysis, factor analysis, multilevel modelling, and social network analysis.

Multiple Correspondence Analysis

Multiple correspondence analysis is the methodological mainstay of Bourdieu’s quantitative investigation. Examples in this regard include his empirical probes into cultural preferences and social classification in Distinction: A Social Critique of the Judgement of Taste (1979); the interplay of social backgrounds, academic reputations, intellectual activities, and political engagements of academics in Homo Academicus (1984); symbolic domination through elite schooling in The State Nobility: Elite Schools in the Field of Power (1989); and the construction of housing market by the state and the critique of rational orthodox economic theory in The Social Structures of the Economy (2000), to just name a few. Throughout these investigations, Bourdieu delves into the structures and configurations of social spaces and the positions and position-takings of agents within these social spaces. Such empirical complexities and dynamics are abstracted into a canonical sociological equation ‘[(habitus) (capital)] + field = practice’ (see p. 95 in Distinction), and this equation is the cornerstone of Bourdieu’s field theory. Owing at least in part to the use of multiple correspondence analysis, Bourdieu generates his field theory to powerfully capture, analyse, and abstract the messy social realities.

Multiple correspondence analysis is an exploratory descriptive statistical modelling for groupings and spatial presentation of such groupings. It can group together social categories (e.g., male versus female, educational qualifications, occupations, income levels, subjective preferences) with certain ‘social proximity.’ It can also group together individuals with relative ‘social homogeneity.’ Socially similar categories or individuals are grouped together as a data cloud and positioned in distance from socially dissimilar categories or individuals. Data clouds are then projected onto a multidimensional plot that visualises social spaces configured by groupings of categories or individuals. Through multiple correspondence analysis, social patternings within social space are modelled and seen. As field theory is concerned with positional relations of individual agents and spatial configurations of social categories, it is epistemologically resonant with multiple correspondence analysis. In Science of Science and Reflexivity (2001; p. 33), Bourdieu acknowledges the epistemological commensurability between the two thinking tools: ‘those familiar with the principles of multiple correspondence analysis will appreciate the affinity between that method of mathematical analysis and thinking in terms of a field.’

While multiple correspondence analysis epistemologically matches Bourdieu’s field theory, it does not go without limitations. One limitation is that multiple correspondence analysis is arbitrarily categorical. It is primarily concerned with categorical variables. When a variable is measured on a continuous scale (e.g., income), the analyst or the model categorises the continuous variable according to certain cutoff values (e.g., quartiles). When a cutoff value is used for categorisation, the data points right below and above the cutoff value are pushed into two different categories arbitrarily, but they are de facto marginally different in value. In this vein, categorisation leads to the loss of details and accuracies in the data because it imposes demarcation on data points that are adjacent by nature. A second limitation is that multiple correspondence analysis is an exploratory quantitative methodology and is unable to test hypotheses statistically. That is to say, results of multiple correspondence analysis are interpreted through extrapolation rather than statistical inference. Social patternings constructed through such interpretation may not actually exist in reality, and there may be social patternings that actually do exist in reality, but multiple correspondence analysis fails to identify. Unable to take stock of statistical significance, the risk of incorrect interpretation is left unevaluated, and the probability of drawing a wrong conclusion remains a mystery.

To the best of my knowledge, Bourdieu himself has never acknowledged, at least not explicitly, the limitations of multiple correspondence analysis. It is unknown whether Bourdieu favours multiple correspondence analysis so much that his scholastic point of view is veiled and biased by his methodological preference, or Bourdieu does not see any needs to discuss the limitations of multiple correspondence analysis. But perhaps most likely, all quantitative methods in Bourdieu’s era except multiple correspondence analysis failed to team with his relational sociology. That Bourdieu is so bound with multiple correspondence analysis throughout his quantitative investigations is historical and historic. It is time to move Bourdieu forward quantitatively. In what follows, I highlight the value of using inferential statistics in Bourdieusian educational research. I say of cluster analysis, factor analysis, multilevel modelling, and social network analysis, which show strong potential to address the limitations of multiple correspondence analysis.

Inferential Statistics

Different from multiple correspondence analysis, inferential statistics is able to come to grips with the probability of error. It shows the likelihood that something may not actually exist in reality, although results suggest the opposite, or that something may indeed exist in reality, although results fail to detect it. A methodological caveat is in order here: inferential statistics should be used in Bourdieusian research with great care, and not all inferential statistical models align with Bourdieusian thinking. Cluster analysis, factor analysis, multilevel modelling, and social network analysis are candidates for use in Bourdieusian research.

Cluster analysis and factor analysis are similar to multiple correspondence analysis in that they aim to explore patterns of groupings. The two analyses can be performed through both a bottom-up, data-driven approach and a top-down, theory-laden approach. The former approach is purely exploratory, looking for whatever number of clusters or factors that would capture the most variance in the data. In contrast, the latter only extracts a certain number of clusters or factors suggested by theory that would best present the variance in the data. Cluster analysis, similar to its ‘higher version sibling models’ such as latent profile analysis and latent class analysis, is able to group individuals together according to similar attributes measured by selected variables. Individuals in the same cluster are more similar to each other than to those in a different cluster. Factor analysis differs in that it groups variables together according to their intercorrelations across all selected individuals. In Bourdieusian terms, cluster analysis is particularly useful to explore the habitus and the capital portfolio of different ‘classes’ of individuals. Factor analysis is particularly useful to explore different dispositions, such as patterns of behaviours and perceptions, of individuals. Nevertheless, cluster analysis and factor analysis require the satisfaction of the statistical assumption of independence of variance. For Bourdieu, the real is relational. In light of this Bourdieusian philosophy, independence of variance cannot be assumed or can never be achieved perfectly in reality.

Multilevel modelling, as its name suggests, situates individuals at different levels. Within each level, individuals are not necessarily independent of one another; rather, they are all socially related. In an educational context, for instance, students in the same classroom may be homogenous in certain ways as they are taught by the same teacher and socialised with the same peers; students in the same school may be homogenous in certain ways as they are exposed to the same school ecology and curriculum; students in the same jurisdiction may be homogenous in certain ways as they are educated up in the same policy context. In Bourdieusian terms, different levels of educational contexts can be understood as subfields within larger fields. Within the same field, individual being, thinking, and doing are driven by habitus and capital, and tend to correspond to the logic of practice of that field. Multilevel modelling is particularly useful to measure the autonomy and heteronomy of subfields to their parent fields. It can also model how individual dispositions (habitus) and social positions (capital) engineer practice in (dis)similar ways across different fields.

Multilevel modelling can be seen as a type of regression analysis, but Bourdieu is intolerant of the failure of regression in questioning the efficacy of the so-called independent variables. In Distinction, Bourdieu (1984, p. 112) asserts that what matters in his relational sociology is ‘a particular configuration of the system of properties’ defined by a whole set of factors ‘operating in all areas of practice such as sex, age, marital status, place of residence.’ That is to say, Bourdieu’s relational sociology probes and probs the intersectionality of the inter-nested variables that, in principle, are not independent of one another. Bourdieu’s criticism of regression for treating variables as independent of one another does not necessarily exclude the use of regression within a Bourdieusian remit. Modern regression analysis can take into account the interaction effect across different variables, which redresses the naïve assumption of the so-called independent variables. Multilevel modelling can include interaction effects in its analysis.

Cluster analysis, factor analysis, and multilevel modelling can address the limitations of multiple correspondence analysis by grappling with both categorical and continuous variables while taking stock of statistical significance. Nevertheless, it is presumptuous to claim that they are utterly superior to multiple correspondence analysis because none of them can visualise spatial configurations and positional oppositions within a field. Herein lies the value of social network analysis in fusing together the methodological merits of multiple correspondence analysis and inferential statistics. In the article ‘A Bourdieusian Rebuttal to Bourdieu’s Rebuttal: Social Network Analysis, Regression, and Methodological Breakthroughs,’ I have made an attempt to incorporate social network analysis into Bourdieusian framing. Here I provide a brief account of some of the important principles.

Throughout his oeuvre, Bourdieu has repeatedly criticised social network analysis and made a clear distinction between network theory and field theory. The former, according to Bourdieu, reduces social reality to interpersonal interactions and inter-subjective ties. Field theory goes beyond substantial realism. It instead delves into relative positions, tendencies of position-takings and power relations behind individual links and situates all these dynamics within a space of differentiation. Bourdieu’s aversion to social network analysis is conspicuous, but we have to historicise Bourdieu’s critique. Social network analysis has advanced so much over the past two decades and has no longer merely focused on social connections. Instead, it enables the examination and visualisation of resource distribution and power imbalance within a matrix of networking among individuals, organisations and social events. Inferential statistical analysis is also made available in social network analysis through QAP – Quadratic Assignment Procedure. In addition, the algorithmic principle of two-mode social network analysis is largely identical to that of multiple correspondence analysis. In brief, there is no fundamental incommensurability between the two approaches.

Final Remarks

Each methodological approach has its own strengths and limitations, and can only fit certain research problems, theoretical stances, and philosophical paradigms. Multiple correspondence analysis is arguably the best possible quantitative method that fits Bourdieu’s empirical investigations, field theory, and relational thinking. But this is only true in Bourdieu’s era. As discussed in the foregoing exposition, statistical models such as cluster analysis, factor analysis, multilevel modelling, and social network analysis are promising approaches that can put Bourdieu to work quantitatively. In concluding this article, I propose a methodological agenda of quantifying Bourdieu in educational research.

Multiple correspondence analysis can be used in the first instance to construct the subject of sociological investigation and the field in question. Social patternings that emerge from multiple correspondence analysis can be further analysed through inferential statistical models such as cluster analysis, factor analysis, and multilevel modelling depending on the foci of investigation and the nature of the research problem. Social network analysis can be used to unearth subjective exchanges and structural forces behind these. Qualitative methods can be incorporated when needed to enrich, explain, deepen, or inform quantitative investigations so that Bourdieu’s methodological pluralism is realised. At the final stage of any Bourdieusian sociological enterprise, it is important to sociologise the sociologists themselves through ‘participant objectivation.’ That is, to turn relational sociological analysis onto the sociological selves reflexively, to objectify the objectifier, and to engage with the sociology of sociology.

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Full Citation Information:
Mu, G. M. (2021). An invitation to quantify Bourdieu in educational research. PESA Agora.

Guanglun Michael Mu

Dr Guanglun Michael Mu is Senior Research Fellow in Queensland University of Technology. He is developing a sociology of resilience through his work with Chinese floating children and left-behind children in migration context; Chinese teachers in inclusive education context; and diverse student populations in Australia’s multicultural context. Michael’s work has been published into five books and numerous papers.