TABLE OF CONTENTS Factor analysis is a multivariate tool that is very similar to PCA. Factor analysis is also used to condense a set of observed variables into a smaller number of transformed variables called components or factors. Both factor analysis and PCA are used to identify an underlying structure or pattern beneath a set of multivariate data. However, the emphasis in factor analysis is on the identification of underlying "factors" that might explain the mutual correlative relationships. Figure 5.28 illustrates the flow chart of factor analysis.
The data set for factor analysis is essentially the same as that for principal component analysis. Factor analysis can be represented by the following equations:
| (5.39) |  |
where
is called the factor loading matrix.
is the vector representing m factors, where Y j is the jth factor, for j = 1, ..., m, m < p, usually m is much smaller than p.
In Eq. (5.37),
represents the error vector that is the difference between original variables and factors, where ? i is called ith specific factor error, for i = 1,..., p.
If we examine Eq. (5.37), we can find that it is very similar to Eq. (5.3), except that in Eq. (5.37), we want to use the vector combination of m factors to approximately represent the original multivariate variables. While in principal component analysis, there are p components; however, we...
