Principal Components and Factor Analysis

Select the Advanced tab of the Define Method of Factor Extraction dialog box to access options that offer a variety of techniques for principal factor analysis as well as principal components analysis.

Extraction method. Select an option button in the Extraction method group box to determine the procedure used for extracting the factors from the correlation matrix.

Principal components. Select the Principal components option button to factor the original correlation matrix (with 1s on the diagonal, i.e., for communalities); all other options will result in principal factor analyses. This distinction is discussed in the Introductory Overviews.

Communalities=multiple R2. If the Communalities=multiple R2 option button is selected, then, prior to factoring, the diagonal of the correlation matrix (communalities) will be computed as the multiple R-square of the respective variable with all other variables. This is a common default method for estimating the communalities for principal factor analysis.

Iterated commun. (MINRES). Select the Iterated commun. (MINRES) option button for this method of factoring, which was originally proposed by Harman & Jones (1966). First, multiple R-square estimates are used for the communalities. After the initial extraction of factors, the method adjusts the loadings over several iterations and evaluates the goodness-of-fit of the resulting solution in terms of the residual sums of squares.

Maximum likelihood factors. Select the Maximum likelihood factors option button for this method of factoring, which was first proposed by Lawley (1940), and is discussed in detail in Harman (1976). Unlike in the other methods, it is assumed that the underlying number of factors is known (that is, as set in the Max. no. of factors box). STATISTICA will then estimate the loadings and communalities that maximize the probability of the observed correlation matrix to occur (hence the term maximum likelihood). A Chi-square test of the goodness-of-fit is available on the Factor Analysis Results - Explained Variance tab.

Centroid method. Select the Centroid method option button for this method of factoring, which was originally developed by Thurstone (1931), and represents a geometrical approach to factor analysis. It is the least "modern" method for factor analysis. Centroid factoring procedures will recompute the communalities in successive iterations. Iterations will continue until either 1) the Maximum no. of iterations is exceeded, or 2) the Min. change in communality is less than that specified in the respective box in the Iterated communalities group box. Refer to Harman (1976) or Wherry (1984) for additional details.

Principal axis method. If the Principal axis method option button is selected, then, in each iteration, the eigenvalues are computed from current communalities; next the communalities are recomputed based on the extracted eigenvalues and eigenvectors. The new communalities are then placed in the diagonal of the correlation matrix, and the next iteration begins. Iterations will continue until either 1) the Maximum no. of iterations is exceeded, or 2) the Min. change in communality is less than that specified in the respective box in the Iterated communalities group box.

Max. no. of factors. Type a number in the Max. no. of factors box to specify how many factors will be extracted. Note that this box works in conjunction with the Mini. eigenvalue box below it; that is, STATISTICA will extract either as many factors as requested, or as many as have eigenvalues greater than that specified in the Mini. eigenvalue box, whichever criterion yields a fewer number of factors.

Mini. eigenvalue. Type a number in the Mini. eigenvalue box to specify how many factors will be extracted. STATISTICA will extract as many factors as there are eigenvalues greater than the number specified in this field. Note that this edit field works in conjunction with the Maximum no. of factors field.

Iterated communalities. The options under Iterated communalities are only available if the Principal axis method or Centroid method option buttons are selected in the Extraction method group box.

Min. change in communality. Principal axis factoring and centroid factoring procedures will recompute the communalities in successive iterations until some criterion is met. Specifically, iterations will stop when the change in the successively computed communalities is less than the value specified in the Min. change in communality box, or when the Maximum no. of iterations have been exceeded.

Maximum no. of iterations. Principal axis factoring and centroid factoring procedures will recompute the communalities in successive iterations; iterations will stop when the change in the successively computed communalities is less than the value specified in the Min. change in communality box, or when the Maximum no. of iterations have been exceeded.