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By Timothy A. Brown PsyD
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Extra resources for Confirmatory Factor Analysis for Applied Research
The factor axes remain at 90° angles, but are rotated in the most optimal fashion to maximize high factor loadings and minimize low loadings. Rotation produces a transformation matrix. Using matrix algebra, the unrotated factor loading matrix is multiplied by the transformation matrix to produce the rotated factor loading matrix. 93347 A. 336 B. 416 C. 4. Geometric representations of unrotated, orthogonally rotated, and obliquely rotated factor matrices. 34 The Common Factor Model and EFA 35 These values convey how much the axes were rotated to foster simple structure.
Another eigenvalue-based procedure for guiding factor selection is parallel analysis (Horn, 1965; Humphreys & Montanelli, 1975). 2. Scree test of eigenvalues from the unreduced correlation matrix. Arrow indicates region of curve where slope changes. 6 Both the observed sample and random data eigenvalues are plotted, and the appropriate number of factors is indicated by the point where the two lines cross. Thus, factor selection is guided by the number of real eigenvalues greater than the eigenvalues generated from the random data; that is, if the “real” factor explains less variance than the corresponding factor obtained from random numbers, it should not be included in the factor analysis.
For instance, the validity of a given factor should be evaluated in part by its interpretability; for example, does a factor revealed by the EFA have substantive importance? A firm theoretical background and previous experience with the variables will strongly foster the interpretability of factors and the evaluation of the overall factor model. Moreover, factors in the solution should be well defined—that is, comprised of several indicators that strongly relate to it. Factors that are represented by two or three indicators may be underdetermined (have poor determinacy, see below) and highly unstable across replications.