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What is multiple correspondence analysis?

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

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What is multiple correspondence analysis?

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

  2. 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

  3. 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).

  4. 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.

  5. The number of dimensions evident in the data is assessed by interpreting eigenvalues and variance rates Step 2: assess number of axes required to interpret the space

  6. Step 3: visualise the ‘cloud of modalities’

  7. Step 4: Superimpose ‘supplementary variables’ to aid interpretation

  8. Step 5: Use cloud of individuals to further aid interpretation

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

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

  11. 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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