Rotation by using Stata

Rotation further simplifies factor structure. After factoring, type rotate followed by an option to specify the type of rotation. Two common types are:

varimax   Varimax orthogonal rotation, producing uncorrelated factors or components (default).

promax( )   Promax oblique rotation, allowing correlated factors or components. Choose a number (promax power) < 4; the higher the number, the greater the degree of inter­factor correlation. promax(3) is the default.

Type help rotate for a complete list of rotation methods and other options. For example:

factors( )   As it does with factor , this option specifies how many factors to retain.

entropy   Minimum entropy orthogonal rotation.

Rotation can be performed following any factor analysis, not just principal component factoring, as will be seen later. This section follows through with our factor, pcf example. For orthogonal (default) rotation of the first two components found in the planetary data, we simply type rotate.

The example above accepts all the defaults: varimax rotation and the same number of factors retained in the last factor. We could have asked for the same rotation explicitly, by adding options to the command: rotate, varimax factors(2).

For oblique promax rotation (allowing correlated factors) of the most recent factoring, type

By default, this example used a promax power of 3. We could have specified the promax power and desired number of factors explicitly:

. rotate, promax(3) factors(2)

promax(4) would permit further simplification of the loading matrix, at the cost of stronger interfactor correlations and less total variance explained.

After promax rotation, rings, lograd, logmoons and logmass load most heavily on factor 1. This appears to be a “large size/many satellites” dimension. logdsun and logdense load higher on factor 2, forming a “far out/low density” dimension. A post-factor-analysis graphing command, loadingplot, helps to visualize these results (Figure 11.2).

Source: Hamilton Lawrence C. (2012), Statistics with STATA: Version 12, Cengage Learning; 8th edition.