Varimax: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
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===Description=== | ===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. | Input loads is a ''N'' by ''K'' matrix with orthogonal columns and the output <tt>vloads</tt> is a ''N'' by ''K'' matrix with orthogonal columns rotated to maximize the "raw varimax criterion". Optional input ''<tt>options</tt>'' 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=== | ===Algorithm=== | ||
Under varimax the total simplicity S is maximized where | Under varimax the total simplicity S is maximized where: | ||
<math>S=\sum_{k=1}^{K}{S_k}</math> | |||
and the simplicty for each factor (column) is <math>S_k = \overline {(a_k-\bar{a}_k)^2}</math> where the overbar indicates the mean and <math>a_k</math> is the ''k''<sup>th</sup> column of <tt>vloads</tt>. | |||
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." | 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." | ||
Latest revision as of 15:31, 19 December 2016
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 kth 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."