Multiple Correspondence Analysis (MCA) Presentation

Data - issues Studying the individuals Studying the categories Interpretation aids
Multiple Correspondence Analysis
François Husson
Applied Mathematics Department - AGROCAMPUS OUEST
[e-mail]
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Data - issues Studying the individuals Studying the categories Interpretation aids
Plan
1Data - issues
2Studying the individuals
3Studying the categories
4Interpretation aids
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Data - issues Studying the individuals Studying the categories Interpretation aids
The data
21
Categorical variables
I
1
i
j
Individuals
1J
vij
Iindividuals
Jqualitative variables
vij : category of the j-th variable
possessed by the i-th individual
Example : survey where Ipeople
reply to Jmultiple-choice questions
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Data - issues Studying the individuals Studying the categories Interpretation aids
The data
17
i’ 0 1 0 0 0
Kj= 5
I
1
i
j
Individuals
1J
i’
I
1
i
j
Individuals
1J
yik
Indicator Matrix
1k KjKΣ
J
IJIpk
I
Categorical variables Categories
vij
married
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Data - issues Studying the individuals Studying the categories Interpretation aids
Goals
1Studying the individuals
One individual = one row of the CDT = set of categories
Similarity of individuals – Inter-individual variability
Principal axes of the inter-individual variability
(in relation to the categories)
2Studying the variables
Links between qualitative variables
(in relation to the categories)
Visualization of the set of associations between categories
Synthetic variables
(quantitative indicators based on the qualitative variables)
⇒Similar problem to PCA
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