The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both…

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem which solves the case of two matrices is given a more straightforward proof. Other considerations in rotating matrices are discussed. (Author/JKS)

A new algorithm to obtain the least squares solution in common factor analysis is presented. It is based on the up-and-down Marquadt algorithm developed by the present authors. Experiments in the use of the algorithm under various conditions are discussed. (Author/JKS)

Two alternating least squares algorithms are presented for the simultaneous components analysis method of R. E. Millsap and W. Meredith (1988). These methods, one for small data sets and one for large data sets, can indicate whether or not a global optimum for the problem has been attained. (SLD)

Joint correspondence analysis is a technique for constructing reduced-dimensional representations of pairwise relationships among categorical variables. An alternating least-squares algorithm for conducting joint correspondence analysis is presented that requires fewer iterations than the algorithm previously proposed by M. J. Greenacre. (SLD)

In FACTALS, an alternating least squares algorithm is used to fit the common factor analysis model to multivariate data. A. Mooijaart (1984) demonstrated that the algorithm is based on an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS. (Author/TJH)

The DEDICOM (decomposition into directional components) model provides a framework for analyzing square but asymmetric matrices of directional relationships among "n" objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straightforward computational solution…

Five techniques that combine the ideals of rotation of matrices of factor loadings to optimal agreement and rotation to simple structure are compared on the basis of empirical and contrived data. Combining a generalized Procrustes analysis with Varimax on the main of the matched loading matrices performed well on all criteria. (SLD)

A model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks. An algorithm is presented for fitting the model to the data by least squares. Examples demonstrate the method. (SLD)

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure. (Author)

An expression is given for weighted least squares estimators of oblique common factors of factor analyses, constrained to have the same covariance matrix as the factors they estimate. A proof of the uniqueness of the solution is given. (Author/JKS)

A new method to estimate the parameters of Tucker's three mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. An example is presented. (Author/JKS)

A data analysis model called CANDELINC performs a broad range of multidimensional data analyses. The model allows for the incorporation of general linear constraints. Several examples are presented. (JKS)