An iterative process is proposed for obtaining an orthogonal simple structure solution. At each iteration, a target matrix is constructed such that the relative contributions of the target majorize the original ones, factor by factor. The convergence of the procedure is proven, and the algorithm is illustrated. (SLD)

Enriching factor rotation algorithms with the capacity to conduct repeated searches from random starting points can make the tendency to converge to optima that are merely local a way to catch rotations of the input factors that might otherwise elude discovery. Use of the HYBALL computer program is discussed. (SLD)

Issues related to the decision of the number of factors to retain in factor analyses are identified. Three widely used decision rules--the Kaiser-Guttman (eigenvalue greater than one), scree, and likelihood ratio tests--are investigated using simulated data. Recommendations for use are made. (Author/JKS)

The performance of four rules for determining the number of components (factors) to retain (Kaiser's eigenvalue greater than one, Cattell's scree, Bartlett's test, and Velicer's Map) was investigated across four systematically varied factors (sample size, number of variables, number of components, and component saturation). (Author/JKS)