Varimax

Purpose

Orthogonal rotation of loadings.

Synopsis

vloads = varimax(loads,options);

Description

Input loads is a N by K matrix with orthogonal columns and the output vloads is a N by K matrix with orthogonal columns rotated to maximize the "raw varimax criterion". Optional input options is discussed below.

Options

Optional input (options) is a structure array with the following fields:

• stopcrit: [ 1e-6 10000 ] stopping criteria

• stopcrit(1) is a relative tolerance { 1e-6 }
• stopcrit(2) is the maximum number of iterations { 10000 }

Algorithm

Under varimax the total simplicity S is maximized where: $S=\sum _{k=1}^{K}{S_{k}}$ and the simplicty for each factor (column) is $S_{k}={\overline {(a_{k}-{\bar {a}}_{k})^{2}}}$ where the overbar indicates the mean and $a_{k}$ is the k^th column of vloads.

The algorithm is based on Kaiser's VARIMAX Method (J.R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Revised Ed., pp 373-376, 1999). They note that if the algorithm converges, "which is not guaranteed, then a (local) maximum ... has been found."

See Also

analysis, pca