User Guide

Chapter
29
Factor Analy
sis
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 c
an 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).
The facto
r analysis procedure offers a high degree of flexibility:
 Seven met
hods of factor extraction are available.
 Five met
hods of rotation are available, including direct oblimin and promax
for nonorthogonal rotations.
 Three methods of computing factor scores are available, and scores can be saved
as variables for further analysis.
Example. What underlying attitudes lead people to respond to the questions on a
politica
l survey as they do? Examining the correlations among the survey items
reveals that there is significant overlap among various subgroups of items—questions
about taxes tend to correlate with each other, questions about military issues correlate
with eac
h other, and so on. With factor analysis, you can investigate the number of
underlying factors and, in many cases, you can identify what the factors represent
conceptually. Additionally, you can compute factor scores for each respondent, which
can the
n be used in subsequent analyses. For example, you might build a logistic
regression model to predict voting behavior based on factor scores.
Statistics. For each variable: number of valid cases, mean, and standard deviation.
For eac
h factor analysis: correlation matrix of variables, including significance
levels, determinant, and inverse; reproduced correlation matrix, including anti-image;
initial solution (communalities, eigenvalues, and percentage of variance explained);
441