# Exploratory factor analysis: Extraction

The Extraction dialog provides options for specifying

- Method
- Allows you to specify the method of factor extraction. Available methods are principal
components, unweighted least squares, generalized least squares, maximum likelihood, principal axis
factoring, alpha factoring, and image factoring.
- Principal components: Correlations/Covariances
- A factor extraction method used to form uncorrelated linear combinations of the observed variables. The first component has maximum variance. Successive components explain progressively smaller portions of the variance and are all uncorrelated with each other. Principal components analysis is used to obtain the initial factor solution. It can be used when a correlation matrix is singular.
- Unweighted least-squares: Correlations
- A factor extraction method that minimizes the sum of the squared differences between the observed and reproduced correlation matrices (ignoring the diagonals).
- Generalized least-squares: Correlations
- A factor extraction method that minimizes the sum of the squared differences between the observed and reproduced correlation matrices. Correlations are weighted by the inverse of their uniqueness, so that variables with high uniqueness are given less weight than those with low uniqueness.
- Maximum likelihood: Correlations
- A factor extraction method that produces parameter estimates that are most likely to have produced the observed correlation matrix if the sample is from a multivariate normal distribution. The correlations are weighted by the inverse of the uniqueness of the variables, and an iterative algorithm is employed.
- Principal axis factoring: Correlations/Covariances
- A method of extracting factors from the original correlation matrix, with squared multiple correlation coefficients placed in the diagonal as initial estimates of the communalities. These factor loadings are used to estimate new communalities that replace the old communality estimates in the diagonal. Iterations continue until the changes in the communalities from one iteration to the next satisfy the convergence criterion for extraction.
- Alpha factoring: Correlations
- A factor extraction method that considers the variables in the analysis to be a sample from the universe of potential variables. This method maximizes the alpha reliability of the factors.
- Image factoring: Correlations/Covariances
- A factor extraction method developed by Guttman and based on image theory. The common part of the variable, called the partial image, is defined as its linear regression on remaining variables, rather than a function of hypothetical factors.

- Extract factors based on
- Provides options for choosing how factors are extracted. You can either retain all factors whose eigenvalues exceed a specified value, or you can retain a specific number of factors.
- Results
- Provides the option of requesting the unrotated factor solution of the
eigenvalues.
- Unrotated factor solution
- Displays unrotated factor loadings (factor pattern matrix), communalities, and eigenvalues for the factor solution.

- Iterations
- The Maximum iterations for convergence settings allows you to specify the maximum number of steps that the algorithm can take to estimate the solution.

## Specifying extraction settings

This feature requires Statistics Base Edition.

- From the menus choose:
- In the Exploratory factor analysis dialog, expand the Additional settings menu and click Extraction.