Rotation in Factor Analysis
Factor analysis is a
popular statistical technique to extract a small number of factors from a
larger set of variables. The relationship of the factors to each other is
determined by the rotation technique selected during the analysis.
Importance
In factor analysis, the
rotated component matrix displays the loadings of variables on factors.
Variables are associated with factors based on high loadings. If the factor
axes are rotated, the loading of a variable on one factor is maximized while
its loading on the other factors is minimized thereby making the factor
structure easier to interpret.
Rotations
When the factor axes are
turned by 90 degrees, the rotation is called orthogonal. When the axes are
turned by some other arbitrary degree the rotation is called oblique. Varimax,
Quartimax and Equamax are types of orthogonal rotations, whereas Direct Oblimin
and Promax are types of oblique rotations.
Considerations
The choice of the
rotation technique depends on whether the researcher expects the underlying
factors to be independent or related. In the former case, orthogonal rotations
would be chosen and in the latter case oblique rotations would be chosen. By
performing either orthogonal or oblique rotation, new factor loading values are
obtained for the variables which are called rotated loadings.
Method
Allow selection of the method of factor
rotation. Available methods are varimax, direct oblimin, quartimax, equamax, or
promax.
• Varimax Method- An orthogonal rotation method that minimizes the
number of variables that have high loadings on each factor. This method
simplifies the interpretation of the factors.
• Direct Oblimin Method- A method for oblique (nonorthogonal) rotation. When
delta equals 0 (the default), solutions are most oblique. As delta becomes more
negative, the factors become less oblique. To override the default delta of 0,
enter a number less than or equal to 0.8.
• Quartimax Method- A rotation method that minimizes the number of factors
needed to explain each variable. This method simplifies the interpretation of
the observed variables.
• Equamax Method- A rotation method that is a combination of the
varimax method, which simplifies the factors, and the quartimax method, which
simplifies the variables. The number of variables that load highly on a factor
and the number of factors needed to explain a variable are minimized.
• Promax Rotation- An oblique rotation, which allows factors to be
correlated. This rotation can be calculated more quickly than a direct oblimin
rotation, so it is useful for large datasets.
Display
Allows including output on the rotated solution, as well as
loading plots for the first two or three factors.
• Rotated Solution- A rotation method must be selected to obtain a
rotated solution. For orthogonal rotations, the rotated pattern matrix and
factor transformation matrix are displayed. For oblique rotations, the pattern,
structure, and factor correlation matrices are displayed.
• Factor Loading Plot- Three-dimensional factor loading plot of the first
three factors. For a two-factor solution, a two-dimensional plot is shown. The
plot is not displayed if only one factor is extracted. Plots display rotated
solutions if rotation is requested.
Maximum Iterations for Convergence
Allow specifying the maximum number of steps that the
algorithm can take to perform the rotation.
This feature requires the Statistics Base option.
From the menus choose: In the Factor Analysis
dialog box, click Rotation.
Varimax
The most popular
rotation technique in factor analysis is Varimax. A Varimax rotation attempts
to simplify the columns of the factor matrix achieving the maximum
simplification when only 1s or 0s are present in the columns of the matrix. It
results in factors that are independent of each other.
Conclusion
It is desirable to
rotate the factor axes during factor analysis because unrotated solutions do
not have a clean factor structure and therefore are difficult to interpret. On
the other hand, rotation changes factor loadings and this may lead to factors
with different meanings dependent on the rotation.
Author-
Manish Lath (14145)
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