Family therapists in trauma-response teams: bringing systems thinking into interdisciplinary fieldwork

Attention to the mental health facets of disaster-preparedness and trauma-response teams has increased considerably over the past decade. As family therapists take part in these efforts, they bring with them a worldview that adds valuable contributions to the nature in which fieldwork is conducted and the manners in which interdisciplinary teams function on the ground. In this article, we present how systems thinking sensitizes trauma workers to a variety of clinical presentations and biopsychosocial complexities inherent in this work. We describe common clinical- and practice-related challenges, alongside practical strategies for effectively dealing with these challenges. We draw upon our experiences as family therapists trained in the field of trauma, and our work as field responders, supervisors and team leaders across a variety of local and large-scale disaster events and contexts.     

The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local minima. It is now shown that, in the single-component case, the assumption can only be violated at saddle points. Chances of Candecomp converging to a saddle point are small but still nonzero.     

Causality in medicine: Towards a theory and terminology

One of the cornerstones of modern medicine is the search for what causes diseases to develop. A conception of multifactorial disease causes has emerged over the years. Theories of disease causation, however, have not quite been developed in accordance with this view. It is the purpose of this paper to provide a fundamental explication of aspects of causation relevant for discussing causes of disease. The first part of the analysis will discuss discrimination between singular and general causality. Singular causality, as in the specific patient, is a relation between a concrete sequence of causally linked events. General causation, e.g. as in disease etiology, means various categories of causal relations between event types. The paper introduces the concept of a reference case serving as a source for causal inference, reaching beyond the concept of general causality. The second part of the analysis provides exemplification of a theory of causation suitable for discussing singular causation. The chain of events that induce a disease state can be identified as effective causal complexes, each complex composed of nonredundant components, which separately contribute to the effect of the complex, without the individual component being necessary or sufficient in itself to produce the effect. In the third part of the analysis the theory is elaborated further. Causes, defined as nonredundant components, can furthermore be differentiated according to their avoidability, according to theories about human error or by the potential of eradication. Multifactorial models of disease creates a need for systematic approaches to causal factors. The paper proposes a taxonomical terminology that serves this purpose.     

Suppressing permutations or rigid planar rotations: A remedy against nonoptimal varimax rotations

Varimax rotation consists of iteratively rotating pairs of columns of a matrix to a maximal sum (over columns) of variances of squared elements of the matrix. Without loss of optimality, the two rotated columns can be permuted and/or reflected. Although permutations and reflections are harmless for each planar rotation per se, they can be harmful in Varimax rotation. Specifically, they often give rise to the phenomenon that certain pairs of columns are consistently skipped in the iterative process, whence Varimax will be terminated at a nonstationary point. The skipping phenomenon is demonstrated, and it is shown how to prevent it.The author is obliged to Henk Kiers for commenting on a previous draft.     

On Green's best linear composites with a specified structure,and oblique estimates of factor scores

Green solved the problem of least-squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix. In the present paper an omission in Green's proof is discussed and resolved. Furthermore, it is shown that some recently published solutions for estimating oblique factor scores are special cases of Green's solution for the case of fixed covariance matrices.     

Explicit candecomp/parafac solutions for a contrived 2 × 2 × 2 array of rank three

Kruskal, Harshman and Lundy have contrived a special 2 × 2 × 2 array to examine formal properties of degenerate Candecomp/Parafac solutions. It is shown that for this array the Candecomp/Parafac loss has an infimum of 1. In addition, the array will be used to challenge the tradition of fitting Indscal and related models by means of the Candecomp/Parafac process.     

Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms

Kroonenberg and de Leeuw (1980) have developed an alternating least-squares method TUCKALS-3 as a solution for Tucker's three-way principal components model. The present paper offers some additional features of their method. Starting from a reanalysis of Tucker's problem in terms of a rank-constrained regression problem, it is shown that the fitted sum of squares in TUCKALS-3 can be partitioned according to elements of each mode of the three-way data matrix. An upper bound to the total fitted sum of squares is derived. Finally, a special case of TUCKALS-3 is related to the Carroll/Harshman CANDECOMP/PARAFAC model.     

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.     

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.