
A command that creates a Configuration object from the selected ContingencyTable object by means of Correspondence analysis.
1. We start with the following transformation of the entries f_{ij}:
h_{ij} = f_{ij} / √ (f_{i+}f_{+j})  √ (f_{i+}f_{+j}) / N, 
where h_{ij} is the entry for a cell in the matrix H with transformed data, f_{i+} is the total count for row i, f_{+j} is the total count for column j and N is the grand total. This can be written in matrix form as:
H = R^{–1/2}FC^{–1/2} – R^{1/2}uu′C^{1/2} / N, 
where R and C are diagonal matrices with the row and column totals, respectively and u a column vector with all elements equal to 1.
2. Next the singular value decomposition of matrix H is performed:
H = K Λ L′, 
where K′K = I, L′L = I, and Λ is a diagonal matrix with singular values.
3. Now the row (X) and column points (Y) can be determined. Three normalizations are possible:
For more details see Gifi (1990), chapter 8.
© djmw, April 7, 2004