Seven EFA extraction techniques are available in SAS. These methods span the range of options commonly used by researchers and include all methods generally available in other common statistical software applications (e.g., SPSS, STATA). Each is further described below.

Principal axes factor (PAF) extraction is a variation of PCA. This method replaces the diagonal elements of the matrix of associations (e.g., correlation or covariance matrix) with the initial communality estimates, or initial estimates of the shared variance. In PCA this substitution does not occur, effectively permitting PCA to estimate components using all of the variance and not just the shared variance, When this substation occurs, it acknowledges the realistic expectation of imperfect measurement and instead uses only the shared variance in the estimation. The final set of factors and communality coefficients are estimated from the revised matrix of associations.

Iterated principal axes factor extraction is identical to PAF, except that an iterative estimation process is used. Each successive estimate of the communality coefficients is used to replace the diagonal of the matrix of associations. The process is repeated iteratively until the communality coefficients stabilizes—or changes less than a predetermined threshold. This extraction technique tends to be favored when multivariate normality of the variables is not a tenable assumption (Fabrigar, Wegener, MacCallum, & Strahan, 1999).

Alpha extraction seeks to maximize the Cronbach’s coefficient alpha estimate of the reliability of a factor. The difference between alpha extraction and other extraction techniques is the goal of the generalization. Maximum likelihood and other similar extraction techniques seek to generalize from a sample to a population of individuals, whereas alpha extraction seeks to generalize to a population of measures. One downside to alpha extraction is that these properties are lost when rotation is used (Nunnally & Bernstein, 1994), applying only to the initial rotation. As we will see in the section on rotation, unrotated results are often not easily interpreted, and this extraction technique is potentially confusing to researchers, who might think they are getting something they are not— if they rotate the results of the alpha extraction.

Maximum likelihood (ML) extraction [4] is another iterative process (used in logistic regression, confirmatory factor analysis, structural equation modeling, etc.) that seeks to extract factors and parameters that optimally reproduce the population correlation (or covariance) matrix. It starts with an assumption that individual variables are normally distributed (leading to multivariate normal distributions with residuals normally distributed around 0). If a certain number of factors are extracted to account for interrelationships between the observed variables, then that information can be used to reconstruct a reproduced correlation matrix. The parameters chosen are tweaked iteratively in order to maximize the likelihood of reproducing the population correlation matrix —or to minimize the difference between the reproduced and population matrices. This technique is particularly sensitive to quirks in the data, particularly in “small” samples, so if the assumptions of normality are not tenable, this is probably not a good extraction technique (Fabrigar et al., 1999; Nunnally & Bernstein, 1994).

Unweighted least squares (ULS) extraction uses a variation on the process of maximum likelihood extraction. It does not make any assumptions about normality and seeks to minimize the error, operationalized as the sum of squared residuals. Between the observed and reproduced correlation (or covariance) matrices, ULS is said to be more robust to non-normal data (as we will see in the third example to come; Nunnally & Bernstein, 1994).

Image extraction and Harris extraction are two methods based on the image factor model, as opposed to the common factor model or the component model (Cattell, 1978, p 403). These methods use a non-iterative process to estimate shared variance (known as the image) and unique variance (known as the anti-image) based on lower-bound estimates of variance produced through multiple regression (Cattell, 1978; Harman, 1967). The image extraction method in SAS corresponds with Guttman’s (1953) version (as opposed to Jöreskog's 1969 version) and the Harris extraction corresponds with Harris’s (1962) Rao-Guttman method. These methods are not very common and will not be discussed any further in the current chapter.

Each of the techniques described above are specified on the METHOD option in the FACTOR procedure. The different extraction methods summarized above can be requested using the following keywords.[5]

method = 
   PRINCIPAL /*PAF extraction*/
   PRINIT /*Iterated PAF extraction*/
   ALPHA /*Alpha extraction*/
   ML /*ML extraction*/
   ULS /*ULS extraction*/
   IMAGE /*Image extraction&/
   HARRIS /*Harris extraction*/

Please note, the PAF and iterated PAF techniques also require the PRIOR S = SMC option (specifying use of the squared multiple correlation matrix for estimation of the initial communalities, as demonstrated in the sample syntax above). If this option is not specified, a PCA will be conducted.