Overview (FACTOR command)

FACTOR performs factor analysis based either on correlations or covariances and using one of the seven extraction methods. FACTOR also accepts matrix input in the form of correlation matrices, covariance matrices, or factor-loading matrices and can write the matrix materials to a matrix data file.

Options

Analysis Phase Options. You can choose to analyze a correlation or covariance matrix using the METHOD subcommand. You can select a subset of cases for the analysis phase using the SELECT subcommand. You can tailor the statistical display for an analysis using the PRINT subcommand. You can sort the output in the factor pattern and structure matrices with the FORMAT subcommand. You can also request scree plots and plots of the variables in factor space on the PLOT subcommand.

Extraction Phase Options. With the EXTRACTION subcommand, you can specify one of six extraction methods in addition to the default principal components extraction: principal axis factoring, alpha factoring, image factoring, unweighted least squares, generalized least squares, and maximum likelihood. You can supply initial diagonal values for principal axis factoring on the DIAGONAL subcommand. On the CRITERIA subcommand, you can alter the default statistical criteria used in the extraction.

Rotation Phase Options. You can control the criteria for factor rotation with the CRITERIA subcommand. On the ROTATION subcommand, you can choose among four rotation methods (equamax, quartimax, promax, and oblimin) in addition to the default varimax rotation, or you can specify no rotation.

Factor Scores. You can save factor scores as new variables in the active dataset using any of the three methods available on the SAVE subcommand.

Matrix Input and Output. With the MATRIX subcommand, you can write a correlation matrix, a covariance matrix, or a factor-loading matrix. You can also read matrix materials written either by a previous FACTOR procedure or by a procedure that writes correlation or covariance matrices.

Basic Specification

The basic specification is the VARIABLES subcommand with a variable list. FACTOR performs principal components analysis with a varimax rotation on all variables in the analysis using default criteria.

• When matrix materials are used as input, do not specify VARIABLES. Use the ANALYSIS subcommand to specify a subset of the variables in the matrix.

• METHOD and SELECT can be specified anywhere. VARIABLES must be specified before any other subcommands, unless an input matrix is specified. MISSING must be specified before ANALYSIS.
• The ANALYSIS, EXTRACTION, ROTATION, and SAVE subcommands must be specified in the order they are listed here. If you specify these subcommands out of order, you may get unexpected results. For example, if you specify EXTRACTION before ANALYSIS and SAVE before ROTATION, EXTRACTION and SAVE are ignored. If no EXTRACTION and SAVE subcommands are specified in proper order, the default will be used (that is, PC for EXTRACTION and no SAVE).
• The FORMAT subcommand can be specified anywhere after the VARIABLES subcommand.
• If an ANALYSIS subcommand is present, the statistical display options on PRINT, PLOT, or DIAGONAL must be specified after it. PRINT, PLOT, and DIAGONAL subcommands specified before the ANALYSIS subcommand are ignored. If no such commands are specified after the ANALYSIS subcommand, the default is used.
• The CRITERIA subcommand can be specified anywhere, but applies only to the subcommands that follow. If no CRITERIA subcommand is specified before EXTRACTION or ROTATION, the default criteria for the respective subcommand are used.

Example

FACTOR VAR=V1 TO V12
  /ANALYSIS=V1 TO V8
  /CRITERIA=FACTORS(3)
  /EXTRACTION=PAF
  /ROTATION=QUARTIMAX.

• The default CORRELATION method is used. FACTOR performs a factor analysis of the correlation matrix based on the first eight variables in the active dataset (V1 to V8).
• The procedure extracts three factors using the principal axis method and quartimax rotation.
• LISTWISE (the default for MISSING) is in effect. Cases with missing values for any one of the variables from V1 to V12 are omitted from the analysis. As a result, if you ask for the factor analysis using VAR=V1 TO V8 and ANALYSIS=ALL, the results may be different even though the variables used in the analysis are the same.

Syntax Rules

• Each FACTOR procedure performs only one analysis with one extraction and one rotation. Use multiple FACTOR commands to perform multiple analyses.
• VARIABLES or MATRIX=IN can be specified only once. Any other subcommands can be specified multiple times but only the last in proper order takes effect.

Operations

• VARIABLES calculates a correlation and a covariance matrix. If SELECT is specified, only the selected cases are used.
• The correlation or covariance matrix (either calculated from the data or read in) is the basis for the factor analysis.
• Factor scores are calculated for all cases (selected and unselected).

• This procedure uses the multithreaded options specified by SET THREADS and SET MCACHE.