# What is multiple correspondence analysis? Mike Savage CRESC & Sociology University of Manchester www.cresc.ac.uk.

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What is multiple correspondence analysis? Mike Savage CRESC & Sociology University of Manchester www.cresc.ac.uk

In a nutshell…. MCA is part of a family of descriptive methods (such as clustering & factor analysis, Principal Components Analysis) which reveal patterning in complex data sets It is distinctive in describing these patterns geometrically by locating each variable/ unit of analysis as a point in a low-dimensional space Is able to map both variables and individuals, so allowing the construction of complex visual maps whose structuring can be interpreted. Offers the potential of linking both variable centred and case centred approaches

Background Mathematical foundations of the Geometric School of Data Analysis laid by French mathematician J-P Benzecri from the 1960s. In sociology, it was popularized by Pierre Bourdieu, notably in Distinction (1979) as a means of unravelling the organisation of cultural fields, but it also lends itself to numerous applications in different disciplines It has been rarely used in Anglophone social science, and appeared to be declining in France. However, the increasing use of visualisations in presentations gives a new opportunity for its use, supported by recent software developments (notably the SPAD Windows interface).

Step 1: define your space Select a range of diverse, but balanced, categorized variables (modalities) in which you seek to elaborate pattern e.g. Cultural Capital and Social Exclusion project used 161 modalities ranging across taste towards and participation in music, film, TV, eating out, visual arts, reading, sport. Rubbish in, rubbish out, very definitely applies.

Step 2: assess number of axes required to interpret the space The number of dimensions evident in the data is assessed by interpreting eigenvalues and variance rates Axis 1Axis 2Axis3Axis 4Axis 5Axis 6 Eigenvalues0.16410.11880.07460.06330.05030.0472 Variance rates5.3333.8602.04162.0561.6341.533 Modified cumulated rates48.270.877.682.0

Step 3: visualise the cloud of modalities

Step 4: Superimpose supplementary variables to aid interpretation

Step 5: Use cloud of individuals to further aid interpretation

Figure 14 : (plane 1-2), L1/L2-Employers in large establishments and Higher managerial positions (n=29)

Figure 15 : (plane 1-2): L13-Routine occupations (n=198)

Conclusions A descriptive method which allows researchers to reveal latent pattern Depends for its effectiveness on crafting careful visualisations. Has unusual capacity to link quantitative and qualitative data in meaningful ways because of its interest in the individual It has the potential to be used alongside other forms of multivariate statistics

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