The African Centre of Excellence for Inequality Research (ACEIR) recently partnered with the Constructor University in Bremen, Germany on their Wealth Data Science Summer School. The two-week program ran simultaneously in Bremen and Cape Town, offering several hybrid sessions on the measurement of wealth and related inequalities.
In Cape Town, ACEIR was fortunate to host renowned sociologists Professor Mike Savage from the London School of Economics (LSE) and Professor Johs Hjellbrekke from the University of Bergen, Norway. Professor Hjellbrekke, an expert in Multiple Correspondence Analysis (MCA), provided a series of lectures and applied sessions on the method to Cape Town participants, including to visiting colleagues and students from the LSE.
This lecture series stemmed from an existing collaboration between Savage, Hjellbrekke and ACEIR team members on the socioeconomic dimensions of racial inequality in South Africa. The interest in better understanding how to use MCA for social science research motivated this Cape Town segment of the summer school. To showcase this method here, I share selected findings from our article, “The socioeconomic dimensions of racial inequality in South Africa” (Branson et al., 2024).
An application to South Africa
Broadly, MCA is a powerful tool for understanding relationships in categorical data. By reducing the dimensionality of the data, MCA makes it easier to visualize and interpret how different variables relate to one another. For example, when applied to socioeconomic variables, MCA can reveal patterns and clusters that show how these factors group together in ‘social space’. Unlike standard regression analysis, which often assumes a predictive relationship between variables, MCA doesn’t make any assumptions. Instead, it lets the data reveal patterns and clusters on its own.
In Branson et al. (2024), we apply MCA to understand social forms of advantage in South Africa, with the aim of uncovering the contemporary structuring of social class. We then explore whether these social classes remain linked to racial divides. Importantly, respondents’ race is not used in the initial structuring of classes, but its importance is explored in a subsequent step.
This work draws on models of ‘social space’ by the French sociologist Pierre Bourdieu (1985), who considered how various forms of capital (economic, cultural, and social) influenced people’s position within the social hierarchy in France. Social space models have since been used – predominantly in the global north – to dissect the multidimensional structuring of privilege.
To construct the South African social space, we use data from Wave 5 of the National Income Dynamics Study (SALDRU, 2018). Specifically, we start with six variables on economic capital (income quintile, property ownership, net worth, computer ownerships, and categories for the number of rooms in the house), three on cultural capital (highest level of own education, highest level of mother’s education, and self-reported proficiency writing in English), and five on social capital (likelihood of a neighbour returning a lost wallet with R200, and trust in: others of the same race, other races, relatives, and others you know, respectively).
Figure 1 presents a biplot (or cloud of categories) derived from the MCA. Interpreting the biplot requires simultaneous consideration of the axes and the points representing categories. The biplot axes represent the two dimensions that capture the most significant variation in the full set of variables taken together. In Branson et al. (2024), the most variation in the data occurs between those with high and those with low economic and cultural capital. Therefore, on the horizontal axis (axis 1), we observe categories related to these forms of capital spread out along the axis. Categories relating to low economic and cultural capital volumes are located on the right, and those relating to high capital volumes are located on the left.
Points representing categories are positioned in a way that reflects the relationships between these categories. If two category points are close to each other, it means that these categories tend to be frequently combined together for individuals (e.g. being in the top income quintile (5) and having a post-school qualification). Conversely, if two category points are far apart, it suggests that these categories rarely occur together. That categories representing high economic and cultural capital frequently occur together among respondents provides visual confirmation of the very strong intersection between economic and cultural capital in South Africa.
Axis 2 is defined by high vs. low volumes of social capital, and we thus see categories related to trust spread out vertically along this axis. Importantly, we can see that categories indicating low volumes of economic and cultural capital are far away from both high and little to no trust, signalling that trust is a divisive force among these respondents. On the other hand, categories indicative of high economic and cultural capital occur relatively more closely to the high trust categories.
Figure 1: Cloud of categories
When age and race categories are overlayed on the biplot, a revealing imagery emerges. Figure 2 shows that White respondents are located on the upper left hand of the plot, amongst respondents with high amounts of economic, cultural and social capital. Black and Coloured respondents are located on the right-hand side. Axis 1 thus also inscribes a hierarchy in terms of racial inequality.
The figure also shows that axis 2 separates the youngest from the oldest respondents. The lowest trust levels are more often found among the youngest respondents and the highest trust levels among the more elderly (70 years+).
Figure 2: Race and age group overlayed on the MCA bi-plot
Respondents can also be plotted along the two axes, thereby creating a cloud of individuals. Again, the proximity of points tells us about the similarity of individuals, as determined by the categories into which respondents fall. An even clearer picture of the significance of racial divides can be seen by projecting race within this space (Figure 3). We draw ellipses containing 86.47%[1] of respondents from each race group, visually exposing the sharpness of the racial divide. White South Africans (the red ellipse) are distinctive. They fall on the left side and are minimally separated on axis 2, indicating that they are much more similar in terms of the levels of trust they articulate than other race groups. There is higher variation in the trust scores for Asian, Coloured and Black individuals for each position on axis 1.
Figure 3: Cloud of individuals with race ellipses
However, White South Africans are not completely separate from the other groups. There is a large overlapping space towards the left-centre, where White respondents are found alongside Asian, Coloured, and Black individuals. There is thus also evidence that there is a certain blurring of the racial divide, which might suggest that racial divides are less definitive in this area of social space. We test this more precisely by performing a cluster analysis on the MCA axes to derive social classes, results of which are presented and discussed here.
In Branson et al. (2024), we conclude that the use of MCA and a social space perspective has offered insights into both the perpetuation yet also the modulation of entrenched forms of privilege. While confirming how entrenched racial inequalities remain among the most advantaged and disadvantaged members of South African society, the cluster analysis also reveals suggestions of fluidity and change among a group situated toward the upper-middle of the social space.
[1] This is +/−2 SDs in a two-dimensional distribution.
References
Bourdieu, P. (1985). Distinction. Routledge.
Branson, N., Hjellbrekke, J., Leibbrandt, M., Ranchhod, V., Savage, M., & Whitelaw, E. (2024). The socioeconomic dimensions of racial inequality in South Africa: A social space perspective. The British Journal of Sociology, 1–23. https://doi.org/10.1111/1468-4446.13115
Southern Africa Labour and Development Research Unit. (2018). National Income Dynamics Study 2017, Wave 5 [dataset]. Version 1.0.0 Pretoria: Department of Planning, Monitoring, and Evaluation [funding agency]. Cape Town: Southern Africa Labour and Development Research Unit [implementer], 2018. Cape Town: DataFirst [distributor]. https://doi.org/10.25828/fw3h-v708