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>>>Advanced Analytics>>Factor Analysis
Let us look at the following example. Suppose we want to measure people's
satisfaction with their lives. We design a satisfaction questionnaire with
various items; among other things we ask our subjects how satisfied they are
with their hobbies and how intensely they are pursuing a hobby. Most likely,
the responses to the two items are highly correlated with each other. Given a
high correlation between the two items, we can conclude that they are quite
redundant.
One can summarize the correlation between two variables in a scatter plot. A
regression line can then be fitted that represents the "best"; summary
of the linear relationship between the variables. If we could define a variable
that would approximate the regression line in such a plot, then that variable
would capture most of the "essence" of the two items. Subjects'
single scores on that new factor, represented by the regression line, could
then be used in future data analyses to represent that essence of the two
items. In a sense we have reduced the two variables to one factor. Note that
the new factor is actually a linear combination of the two variables.
The example described above, combining two correlated variables into one factor,
illustrates the basic idea of factor analysis or of principal components
analysis to be precise. If we extend the two-variable example to multiple
variables, then the computations become more involved, but the basic principle
of expressing two or more variables by a single factor remains the same.
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