Factor Analysis
Factor analysis attempts to identify underlying variables, or
factors, that explain the pattern of correlations within a set of observed
variables. Factor analysis is often used in data reduction to identify a small
number of factors that explain most of the variance observed in a much larger
number of manifest variables. Factor analysis can also be used to generate
hypotheses regarding causal mechanisms or to screen variables for subsequent
analysis (for example, to identify collinearity prior to performing a linear
regression analysis).
Types of factor analysis
Exploratory factor analysis seeks to uncover the underlying structure of a
relatively large set of variables. The researcher's assumption is that any
indicator may be associated with any factor. This is the most common form of
factor analysis.
Confirmatory factor analysis seeks to determine if the
number of factors and the loadings of measured (indicator) variables on them
conform to what is expected on the basis of pre-established theory.
Factor Rotation
Factor rotation is an important tool in factor analysis. 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 it is loading on the other factors is minimized
thereby making the factor structure easier to interpret.
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.
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.
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.
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.
Naquib Ahmed
Group-A
Operations
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