TABLE OF CONTENTS One of the most important issues in using factor analysis is its interpretation. Factor analysis often uses factor rotation to enhance its interpretation. Factor rotation can be expressed by the following:
| (5.57) |  |
where T = T m m is called a rotation matrix. T is also an orthogonal matrix, that is, TT T = I. Therefore,
| (5.58) |  |
So if we use 
to replace L as the factor loading matrix, it will have the same ability to represent the correlation matrix ?.
After rotation
| (5.59) |  |
where 
is the new rotated factor loading matrix and 
is the new rotated factor. The new factor 
will also be a standard normal vector such that 
This is because that if 
will also be multivariate normal random variable, 
due to the fact that T is an orthogonal matrix.
The purpose of rotation is to make the rotated factor loading matrix 
have some desirable properties. There are two kinds of rotations. One is to rotate the factor loading matrix such that the rotated matrix 
will have a simple structure. The other is called procrustes rotation, which is trying to rotate the factor matrix to a target matrix. We will discuss these two rotations in subsequent subsections.
Thurstone (1947) suggested the following criteria for simple structure:
Each row of 
should contain at least one zero.
Each column...
