8.2.1 Rotation of configuration

Rotation with principal axes

The configuration is rotated so that successive dimensions account for the maximum possible variance. The symmetric matrix ATA of dimensions (p ´ p) is computed and eigenvectors P of ATA are determined, using Jacobi’s diagonalization method.

The matrix A is transformed into a matrix B of bis elements, such that B = APp, B having n rows and p columns like the matrix A.

Rotated Configuration

The rotation can be performed only on two dimensions at a time. It is up to the researcher to select the dimensions and the angle f of rotation.

ail =

The calculations are performed for each value of i (variable) and as many times as there are variables.

Varimax rotation

The elements ais of A are normalized by the square roots of the communalities corresponding to each variable. Define

Having constructed B =, find the best projection axes for the variables, after equalization of their inertia. Define the function

The maximization of the function Ve is performed through successive rotations of two dimensions at a time, until convergence is reached.

The resulting matrix B of bis elements has the same number of rows and columns as the initial matrix A.

The module Config also computes the matrices of Scalar products and Inter-point distances. These metrics are computed by the following formulae:

Matrix of Inter-point distances:

This is a square and symmetric matrices of Euclidean distances between variables.

Matrix of scalar products

The matrix SP is a square and symmetric matrix of scalar products of variables. If each variable is centered and normalized (mean = 0, standard deviation = 1), then the matrix SP becomes a correlation matrix.