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: and the simplicty for each factor (column) is where the overbar indicates the mean and 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."