Fitting the off-diagonal dedicom model in the least-squares sense by a generalization of the harman and jones minres procedure of factor analysis

Harshman's DEDICOM model providesa framework for analyzing square but asymmetric materices of directional relationships amongn objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straight-forward computational solution for this model is offered in the present paper. The solution can be interpreted as a generalized Minres procedure suitable for handing asymmetric matrices.     

Convergence properties of an iterative procedure of ipsatizing and standardizing a data matrix,with applications to parafac/candecomp preprocessing

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution. This solution need not be centered row-wise if the limiting point of the interations is a matrix of rank one. The results of the present paper bear directly on several types of preprocessing methods in Parafac/Candecomp.     

Control and Responsibility: Taking a Closer Look at the Work of Ensuring Well-Being in Neoliberal Schools

This paper argues that the neo-liberal work of schooling includes a focus on producing subjectivities with a high level of well-being. This is done by drawing on evidence based therapeutic techniques that are adjusted to a school setting. These are termed ‘therapeutic socio-educational technologies. It is argued that these practices adhere to the neo-liberal logic of increased competition, standardization and testing, focusing on the individual child. There are a number of problems connected to these well-being enhancing technologies. These include the risk of producing passive and submissive subjectivities, that are understood as needing therapy by default; pathologizing the discomfort and struggles that are an inherent part of learning; the fragmentation of the child, focusing directly on the child rather than on the content matter at hand; producing an overly mechanic and technified pedagogy, focusing on output, as well as laying claim to much control in a risk-filled relational endeavor.     

Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices

A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled from a continuous distribution, and the third component matrix has full column rank. In this context, we obtain almost sure sufficient uniqueness conditions for the Candecomp/Parafac and Indscal models separately, involving only the order of the three-way array and the number of components in the decomposition. Both uniqueness conditions are closer to necessity than the classical uniqueness condition by Kruskal. Part of this research was supported by (1) the Flemish Government: (a) Research Council K.U. Leuven: GOA-MEFISTO-666, GOA-Ambiorics, (b) F.W.O. project G.0240.99, (c) F.W.O. Research Communities ICCoS and ANMMM, (d) Tournesol project T2004.13; and (2) the Belgian Federal Science Policy Office: IUAP P5/22. Lieven De Lathauwer holds a permanent research position with the French Centre National de la Recherche Scientifique (C.N.R.S.). He also holds an honorary research position with the K.U. Leuven, Leuven, Belgium.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

Quantitative genetic analysis of latent growth curve models of cognitive abilities in adulthood

Though many cognitive abilities exhibit marked decline over the adult years, individual differences in rates of change have been observed. In the current study, biometrical latent growth models were used to examine sources of variability for ability level (intercept) and change (linear and quadratic effects) for verbal, fluid, memory, and perceptual speed abilities in the Swedish Adoption/Twin Study of Aging. Genetic influences were more important for ability level at age 65 and quadratic change than for linear slope at age 65. Expected variance components indicated decreasing genetic and increasing nonshared environmental variation over age. Exceptions included one verbal and two memory measures that showed increasing genetic and nonshared environmental variance. The present findings provide support for theories of the increasing influence of the environment with age on cognitive abilities.     

A generalization of Verhelst's solution for a constrained regression problem in alscal and related MDS-algorithms

Verhelst derived a solution for a constrained regression problem which occurs in the interval measurement application of ALSCAL and related MDS-algorithms. In the present paper it is shown that Verhelst's solution is based on an implicit nonsingularity assumption. A general solution, which contains Verhelst's solution as a special case, is derived by a simple completing-the-squares type approach instead of partial differentiation with a Lagrange multiplier. In addition, this approach permits the identification of a small interval which uniquely contains the optimal value of a parameter needed to solve the special case where Verhelst's solution is valid.The author is obliged to Dirk Knol and Klaas Nevels for helpful comments.     

Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.     

Correlation coefficients for more than one scale type: An alternative to the Janson and Vegelius approach

Janson and Vegelius have recently suggested a family of correlations for variables of mixed scale types, including nominal scales. The resulting correlations areE-coefficients, which means that they are unity if the variables involved are identical up to permissible transformations, and that they can be considered as inner products in a Euclidian space. Some of the coefficients of the correlation family suggested by Janson and Vegelius are generalized squared product-moment correlations and some are not. In the present paper, a family of correlations for variables of mixed scale types is advocated all members of which are generalized squared product-moment correlations. Some practical advantages of the latter family are explained. The authors are obliged to Klaas Nevels and Henk Kiers for helpful comments.