Replication of Factors in Variations on a Synthetic Correlation Matrix

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Abstract
A factor replication procedure (FACTOREP) which provides a solution to the number of factors problem for multiple scale questionnaires was evaluated using four psychometrically equivalent synthetic correlation matrices containing an imposed three-subscale structure. Comparisons of the structure revealed by two, three, four and nine-factor rotations using the FACTOREP procedure, clearly showed that only the three factor solutions were replicable across all four matrices. An examination of the patterns of factor loadings themselves confirmed the superior replicability of the three-factor solutions and showed that in every case the three factors found were those originally imposed on the matrices.