Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

Proposes an index for assessing the degree of factor simplicity in the context of principal components and exploratory factor analysis. The index does not depend on the scale of the factors, and its maximum and minimum are related only to the degree of simplicity in the loading matrix. (SLD)

Proposes a rescaled Bartless-corrected statistic for evaluating the number of factors in exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures. (SLD)

Proposes a special rotation procedure for the exploratory dynamic factor model for stationary multivariate time series. The rotation procedure applies separately to each univariate component series of a q-variate latent factor series and transforms such a component, initially represented as white noise, into a univariate moving-average.…

H. Kaiser (1992) has shown that the sum of coefficients alpha of a set of principal components does not change when the components are transformed by an orthogonal rotation. In this paper, the rotational invariance and the successive alpha-optimality are integrated and generalized in a simultaneous approach. (SLD)

Identifies a general algorithm for orthogonal rotation and shows that when an algorithm parameter alpha is sufficiently large, the algorithm converges monotonically to a stationary point of the rotation criterion from any starting value. Introduces a modification that does not require a large alpha and discusses the use of this modification as a…

Presents a construction method for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Illustrates that variable elimination can have a large effect on the seriousness of factor indeterminacy. (SLD)