Factor Analysis Extraction
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 Analysis. 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 Method. 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 Method. 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 Method. 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. 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. 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. 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.
Analyze. Allows you to specify either a correlation matrix or a covariance matrix.
- Correlation matrix. Useful if variables in your analysis are measured on different scales.
- Covariance matrix. Useful when you want to apply your factor analysis to multiple groups with different variances for each variable.
Extract. You can either retain all factors whose eigenvalues exceed a specified value, or you can retain a specific number of factors.
Display. Allows you to request the unrotated factor solution and a scree plot of the eigenvalues.
- Unrotated Factor Solution. Displays unrotated factor loadings (factor pattern matrix), communalities, and eigenvalues for the factor solution.
- Scree plot. A plot of the variance that is associated with each factor. This plot is used to determine how many factors should be kept. Typically the plot shows a distinct break between the steep slope of the large factors and the gradual trailing of the rest (the scree).
Maximum Iterations for Convergence. Allows you to specify the maximum number of steps that the algorithm can take to estimate the solution.
To Specify Extraction Options
This feature requires the Statistics Base option.
- From the menus choose:
- In the Factor Analysis dialog box, click Extraction.