Factor Analysis

Factor analysis is used to explain relationships among several, difficult to interpret, and correlated variables using a few, conceptually meaningful, and relatively independent factors. It does so by assessing the underlying relationships or dimensions in the data and replacing them with fewer variables.

To perform a factor analysis of the data:

1	Choose Analysis > Factor Analysis to display the Factor Analysis dialog box.

2	Enter an initial figure for the number of factors you want to use to explain the relationships. This number can be changed to repeat the analysis, as desired.

3	Select the factor analysis method from one of three choices:

4	Principal Component —The principal component model of factor analysis. Direct calculation; no iterations.

Principal Factor—Principal factor analysis. Direct calculation; no iterations.

Unweighted Least Squares—A method of factor analysis using an iterative process. This methods is also knows as minres or the minimum residual method.

5	Optionally, select a rotation type or accept the default of None.

6	Optionally, choose the Iteration Control button (upper right) to fine tune the Unweighted Least Squares and Rotation functions.

7	Click OK to perform the factor analysis.

The results of the analysis are automatically displayed in the Factor Loadings folder.

Two tables are generated in the Factor Loadings folder. The first table contains the factor loadings, which represent the loadings (correlations) that relate each model parameter to each of the derived factors. This table also has a column called Communality, always displayed at the far right part of the table. This field shows the variance explained by all of the factors for a single parameter.

The top portion of the Factor Loading folder displays the data in a color-coded format. Factor Group data, one group per row, is displayed in a red font. Dominant Parameter data, one dominant parameter per column, is displayed with a blue background.

The second table has three fields:

Variance. Presents a summary of the variances associated with each factor. For example, a variance of 3.45 indicates that the factor accounts for as much variance in the data collection as would 3.45 variables, on average.

% Variance. Shows how much of the variance of all the parameters is explained by a single factor.

Cumulative %. Shows how much of the variance of all the parameters is explained cumulatively by from one to all of the factors. That is, as you move left to right in the table, the percentage increases as more and more factors are included.