An empirical sampling distribution of the statistic average trace (E'E) for various orders of A matrices was developed through a Monte Carlo approach. A method is presented which can be used as a guideline in determining whether factor structures obtained from two data sets are congruent. (Author/DEP)

In this paper a rather general theory of oblique factor rotation is outlined. The main results are formulated as four theorems. Necessary and sufficient conditions are derived for two factor matrices to admit identical factor structures and/or factor patterns with factors having unit variances. These conditions are expressed in terms of…

Procedures for assessing the invariance of factors across data sets often use the least squares criterion, which appears to be too restrictive. Tucker's coefficient of congruence is proposed as an alternative. A method that maximizes the sum of the coefficients of congruence between two matrices of loadings is presented. (Author/JKS)

Procrustes rotation involves fitting a factor pattern matrix to a specified target matrix in factor analysis. These rotations are useful for the investigator who wishes to see how well his data can be made to fit a hypothesized factor pattern matrix. The mathematical problems involved in these transformations are outlined and computer algorithms…

The problem considered is that of an investigator sampling two or more correlation matrices and desiring to fit a model where a factor pattern matrix is assumed to be identical across samples and we need to estimate only the factor covariance matrix and the unique variance for each sample. A flexible, least squares solution is worked out and…