Factor Analysis
The main applications of factor analytic techniques are
1) to reduce the number of variables and 2) to detect structure in the
relationships between variables, that is to classify variables. Therefore,
factor analysis is applied as
a data reduction or (exploratory) structure detection method (the term
factor analysis was first introduced by Thurstone, 1931, although similar
techniques were used by Spearman as early as 1904 in his classic research
on the nature of intelligence).
For 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 (item 1) and how intensely they are pursuing a hobby (item
2). 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 scatterplot. 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.
Factor Analysis
is an exploratory
method; for information in Confirmatory Factor
Analysis, see SEPATH. For more information on Factor Analysis, see the Factor
Analysis Overviews.