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 fij:
|hij = fij / √ (fi+f+j) - √ (fi+f+j) / N,|
where hij is the entry for a cell in the matrix H with transformed data, fi+ 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–1/2FC–1/2 – R1/2uu′C1/2 / 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