Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

Detection of words versus good old counting: A note on Mizrahi and Dickinson, “The analytic-continental divide in philosophical practice”

In a recent Metaphilosophy article, Moti Mizrahi and Michael Dickinson argue against characterizing the divide between analytical and continental philosophy as a divide in the use of arguments. This hypothesis is rejected on the basis of a text-mining approach. The present paper argues that the results they extracted do not answer the questions they set out to answer as well as would have been possible. This is due to Mizrahi and Dickinson's choice to disregard duplicate occurrences of argument word pairs, their main indicator for the occurrence of arguments in articles. This paper reconstructs their method by now also counting duplicates. A small corpus (n = 436) of recent (2015–2021) analytical and continental articles is used to rerun the experiment; the results oppose Mizrahi and Dickinson's and suggest that arguments (as operationalized by Mizrahi and Dickinson) occur more in analytical articles. The paper argues that part of the discrepancy derives from the specific methodological choices they made.     

Ten principles of counselling: Grounded theory in a mixed methods research project

This grounded theory (GT) study is part of an extensive mixed methods research project to develop general principles for counselling. Nine hundred counselling protocols were examined. The material is characterised by a quantitative amount of data with a qualitative character. The research is based on the systemic-constructivist research paradigm. The variety of perspectives is an important aspect of the work. Therefore, it is important that the entire research process with GT takes place in exchange with other research settings in order to minimise the limitations caused by the perspective of the researchers. During the research process, there was an intensive examination of GT in order to adapt it to the research project. By using the GT to analyse the extensive qualitative material, the actions of the counsellors were observed and 10 counselling principles were developed. This article presents the research process and the findings.     

Grading the ‘cultural literacy’ project

The essay examines the argument advanced by E.D. Hirsch, Jr., for instituting ‘cultural literacy’ as a fundamental priority of schools. A number of confusions and equivocations in Hirsch's reasoning are identified, and the propensity of his project to indoctrinate is exposed. Among the features of Hirsch's argument shown to be troubling are his shifting construal of ‘language’, his inconsistency about the requirements of cultural literacy, and his uncritical relation to traditional images of the American past and present. The upshot is to raise the question why Hirsch's project has elicited wide support and praise.     

Referenzsemantik in der Partnermodellierung

How can we explain that an assertion on something perceived can be understood in the same manner by somebody who cannot perceive that scene? This problem bases the interest in computational linguistics in how listener modeling could possibly be harmonized with reference semantics. Mental images substituting real perception appear as a way out. The architecture of the listener model has to be adapted to the creation and use of such pictorial data structures. Furthermore, the relation between the latter and a verbal (i. e., propositional) representation must be understood. The resulting architecture of a listener model with reference semantics can be employed to solve communicational problems from three general classes in a better way, as is demonstrated by an example implementation.