15.8 FACTOR

FACTOR  {
         VARIABLES=var_list,
         MATRIX IN ({CORR,COV}={*,file_spec})
        }

        [ /METHOD = {CORRELATION, COVARIANCE} ]

        [ /ANALYSIS=var_list ]

        [ /EXTRACTION={PC, PAF}]

        [ /ROTATION={VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(k)], NOROTATE}]

        [ /PRINT=[INITIAL] [EXTRACTION] [ROTATION] [UNIVARIATE] [CORRELATION] [COVARIANCE] [DET] [KMO] [AIC] [SIG] [ALL] [DEFAULT] ]

        [ /PLOT=[EIGEN] ]

        [ /FORMAT=[SORT] [BLANK(n)] [DEFAULT] ]

        [ /CRITERIA=[FACTORS(n)] [MINEIGEN(l)] [ITERATE(m)] [ECONVERGE (delta)] [DEFAULT] ]

        [ /MISSING=[{LISTWISE, PAIRWISE}] [{INCLUDE, EXCLUDE}] ]

The FACTOR command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find common factors in the data or for data reduction purposes.

The VARIABLES subcommand is required (unless the MATRIX IN subcommand is used). It lists the variables which are to partake in the analysis. (The ANALYSIS subcommand may optionally further limit the variables that participate; it is useful primarily in conjunction with MATRIX IN.)

If MATRIX IN instead of VARIABLES is specified, then the analysis is performed on a pre-prepared correlation or covariance matrix file instead of on individual data cases. Typically the matrix file will have been generated by MATRIX DATA (see MATRIX DATA) or provided by a third party. If specified, MATRIX IN must be followed by ‘COV’ or ‘CORR’, then by ‘=’ and file_spec all in parentheses. file_spec may either be an asterisk, which indicates the currently loaded dataset, or it may be a file name to be loaded. See MATRIX DATA, for the expected format of the file.

The /EXTRACTION subcommand is used to specify the way in which factors (components) are extracted from the data. If PC is specified, then Principal Components Analysis is used. If PAF is specified, then Principal Axis Factoring is used. By default Principal Components Analysis is used.

The /ROTATION subcommand is used to specify the method by which the extracted solution is rotated. Three orthogonal rotation methods are available: VARIMAX (which is the default), EQUAMAX, and QUARTIMAX. There is one oblique rotation method, viz: PROMAX. Optionally you may enter the power of the promax rotation k, which must be enclosed in parentheses. The default value of k is 5. If you don’t want any rotation to be performed, the word NOROTATE prevents the command from performing any rotation on the data.

The /METHOD subcommand should be used to determine whether the covariance matrix or the correlation matrix of the data is to be analysed. By default, the correlation matrix is analysed.

The /PRINT subcommand may be used to select which features of the analysis are reported:

• UNIVARIATE A table of mean values, standard deviations and total weights are printed.
• INITIAL Initial communalities and eigenvalues are printed.
• EXTRACTION Extracted communalities and eigenvalues are printed.
• ROTATION Rotated communalities and eigenvalues are printed.
• CORRELATION The correlation matrix is printed.
• COVARIANCE The covariance matrix is printed.
• DET The determinant of the correlation or covariance matrix is printed.
• AIC The anti-image covariance and anti-image correlation matrices are printed.
• KMO The Kaiser-Meyer-Olkin measure of sampling adequacy and the Bartlett test of sphericity is printed.
• SIG The significance of the elements of correlation matrix is printed.
• ALL All of the above are printed.
• DEFAULT Identical to INITIAL and EXTRACTION.

If /PLOT=EIGEN is given, then a “Scree” plot of the eigenvalues is printed. This can be useful for visualizing the factors and deciding which factors (components) should be retained.

The /FORMAT subcommand determined how data are to be displayed in loading matrices. If SORT is specified, then the variables are sorted in descending order of significance. If BLANK(n) is specified, then coefficients whose absolute value is less than n are not printed. If the keyword DEFAULT is specified, or if no /FORMAT subcommand is specified, then no sorting is performed, and all coefficients are printed.

You can use the /CRITERIA subcommand to specify how the number of extracted factors (components) are chosen. If FACTORS(n) is specified, where n is an integer, then n factors are extracted. Otherwise, the MINEIGEN setting is used. MINEIGEN(l) requests that all factors whose eigenvalues are greater than or equal to l are extracted. The default value of l is 1. The ECONVERGE setting has effect only when using iterative algorithms for factor extraction (such as Principal Axis Factoring). ECONVERGE(delta) specifies that iteration should cease when the maximum absolute value of the communality estimate between one iteration and the previous is less than delta. The default value of delta is 0.001.

The ITERATE(m) may appear any number of times and is used for two different purposes. It is used to set the maximum number of iterations (m) for convergence and also to set the maximum number of iterations for rotation. Whether it affects convergence or rotation depends upon which subcommand follows the ITERATE subcommand. If EXTRACTION follows, it affects convergence. If ROTATION follows, it affects rotation. If neither ROTATION nor EXTRACTION follow a ITERATE subcommand, then the entire subcommand is ignored. The default value of m is 25.

The MISSING subcommand determines the handling of missing variables. If INCLUDE is set, then user-missing values are included in the calculations, but system-missing values are not. If EXCLUDE is set, which is the default, user-missing values are excluded as well as system-missing values. This is the default. If LISTWISE is set, then the entire case is excluded from analysis whenever any variable specified in the VARIABLES subcommand contains a missing value.

If PAIRWISE is set, then a case is considered missing only if either of the values for the particular coefficient are missing. The default is LISTWISE.