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I have a dataset with 28 ordinal variables and 1402 individuals and I am tasked to apply MCA method to create a socio-economic score SES in order to assign individuals into socio-economic groups based on the association patterns of their answers to the 28 questions/variables.

After coding the dataset using R and applying MCA using the indicator method, I have the results of the inertia percentages:

  • 11.6% for the first dimension and
  • 6.3% for the second dimension.

However, using the Burt method, I get

  • 44% for the first dimension and
  • 16% for the second dimension.

What is the difference between the two methods?

Which method should I be using for the interpretation of my results?

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2 Answers 2

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A Burt table is a square matrix of dimension $K \times K$, where each row and each column correspond to one of the categories $K$ of the set of variables. In the generic cell $(i,j)$ we observe the number of individuals who carry both categories $i$ and $j$.

You can see the Burt table as an extension of the contingency table where there are more than two categorical variables.

Correspondence analysis of this table is used to represent the categories. As this table is symmetrical, the representation of the cloud of row profiles is identical to that of the cloud of column profiles and only one of the representations is retained.

However, the inertias associated with each component differ by a coefficient of $\lambda_s$. When $\lambda_s$ is the inertia of $s$ for the MCA, the inertia of component $s$ for a CA of the Burt table will be $λ_s^2$. Furthermore, the percentages of inertia associated with the first components of the CA of the Burt table are higher than the percentages of inertia associated with the first components of the MCA alone.

The Burt table is therefore useful in terms of data storage. Rather than conserving the complete table of individuals $\times$ variables, it is sufficient to construct a Burt table containing the same information in terms of associations between categories, which are considered in pairs with a view to conducting the principal component method. When dealing with a very large number of individuals, the individual responses are often ignored in favour of the associations between categories.

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Would recommend you all to watch this video. Very illustrative with a concrete example :

https://www.youtube.com/watch?v=MyMr1Yn7ntQ

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