Brian O'Connor   UBCO Psychology   UBCO  


SAS, SPSS, and MATLAB Programs for Extension Analysis


O'Connor, B. P. (2001). EXTENSION: SAS, SPSS, and MATLAB programs for extension analysis. Applied Psychological Measurement, vol. 25, p. 88.

Scale development using popular statistical software packages often produces results that are baffling or misunderstood by many users, which can lead to inappropriate substantive interpretations and item selection decisions. High internal consistencies do not indicate unidimensionality; item-total correlations are inflated because each item is correlated with its own error as well as the common variance among items; and the default number-of-eigenvalues-greater-than-one rule, followed by principal components analysis and varimax rotation, produces inflated loadings and the possible appearance of numerous uncorrelated factors for items that measure the same construct (Gorsuch, 1997a, 1997b). Concerned investigators may then neglect the higher order general factor in their data as they use misleading statistical output to trim items and fashion unidimensional scales.

These problems can be circumvented in exploratory factor analysis by using more appropriate factor analytic procedures and by using extension analysis as the basis for adding items to scales. Extension analysis provides correlations between nonfactored items and the factors that exist in a set of core items. The extension item correlations are then used to decide which factor, if any, a prospective item belongs to. The decisions are unbiased because factors are defined without being influenced by the extension items. One can also examine correlations between extension items and any higher order factor(s) in the core items. The end result is a comprehensive, undisturbed, and informative picture of the correlational structure that exists in a set of core items and of the potential contribution and location of additional items to the structure.

Extension analysis is rarely used, at least partly because of limited software availability. Furthermore, when it is used, both traditional extension analysis and its variants (e.g., correlations between estimated factor scores and extension items) are prone to the same problems as the procedures mentioned above (Gorsuch, 1997a, 1997b). However, Gorusch (1997b) recently described how diagonal component analysis can be used to bypass the problems and uncover the noninflated and unbiased extension variable correlations -- all without computing factor scores.

The SAS, SPSS, and MATLAB programs below perform the recommended factor and extension analyses. Users enter their specifications at the start of the programs, which then read and process raw data files (cases by variables). Users specify the procedure for determining the number of factors (parallel analysis, the minimum average partial test, the number of salient loadings procedure, the standard error scree test, the number of eigenvalues great than one rule, or a user-determined number of factors), the factor extraction procedure (common factor analysis, principal components analysis, maximum likelihood factor analysis, or image analysis), and the factor rotation procedure (promax or varimax). Users also choose between regular and higher-order factor analysis. The factor and extension analysis results are then displayed.

The computations for the EXTENSION programs are performed within the matrix processing environments that are provided by SAS (Proc IML), SPSS (Matrix--End Matrix), and MATLAB.


Gorsuch, R. L. (1997a). Exploratory factor analysis: Its role in item analysis. Journal of Personality Assessment, 68, 532-560.

Gorsuch, R. L. (1997b). New procedure for extension analysis in exploratory factor analysis. Educational and Psychological Measurement, 57, 725-740.


Brian P. O'Connor
Department of Psychology
University of British Columbia - Okanagan
Kelowna, British Columbia, Canada