Some clarifications of the TUCKALS2 algorithm applied to the IDIOSCAL problem

Kroonenberg and de Leeuw have suggested fitting the IDIOSCAL model by the TUCKALS2 algorithm for three-way components analysis. In theory, this is problematic because TUCKALS2 produces two possibly different coordinate matrices, that are useless for IDIOSCAL unless they are equal. Kroonenberg has claimed that, when IDIOSCAL is fitted by TUCKALS2, the resulting coordinate matrices will be identical. In the present paper, this claim is proven valid when the data matrices are semidefinite. However, counterexamples for indefinite matrices are also constructed, by examining the global minimum in the case where the data matrices have the same eigenvectors. Similar counterexamples have been considered by ten Berge and Kiers in the related context of CANDECOMP/PARAFAC to fit the INDSCAL model.     

Constrained DEDICOM

The DEDICOM method for the analysis of asymmetric data tables gives representations that are identified only up to a nonsingular transformation. To identify solutions it is proposed to impose subspace constraints on the stimulus coefficients. Most attention is paid to the case where different subspace constraints are imposed on different dimensions. The procedures are discussed both for the case where the complete table is fitted, and for cases where only offdiagonal elements are fitted. The case where the data table is skew-symmetric is treated separately as well.The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant. The authors are obliged to Richard A. Harshman for helpful comments on an earlier version.     

A monotonically convergent algorithm for factals

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.The authors are obliged to Jos ten Berge for stimulating comments on an earlier version of this paper. The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant.     

Processing novel compounds: Evidence for interactive meaning activation of ambiguous nouns

In three experiments, the meaning activation of ambiguous nouns in novel nominal compounds was investigated. Ambiguous nouns were unbalanced homographs occurring as the second members of the compound. Meaningful interpretations of the compounds were based on either the dominant or the subordinate meaning of the ambiguous noun. In Experiment 1, visually presented novel compounds serving as primes were followed at varying intervals by targets associatively related to distinct meanings of the ambiguous noun. In a lexical decision task, facilitation effects were found only for targets related to the meaning that was relevant for the interpretation of the compound. Experiment 2 showed that interactive activation could not be attributed to differences in semantic relatedness between the first members of compounds and targets. Experiment 3 demonstrated equal intralexical relatedness between members for both types of compounds. It is proposed that interactive activation may facilitate the interpretation of the novel compound. Compatible meaning aspects of the nouns may become more strongly activated, and incompatible meaning aspects may not become activated. The selection of meaning aspects relevant for interpretation would thereby be simplified.     

The interpretation of isolated novel nominal compounds

The lexical decision task was used to investigate interpretative processing of isolated novel compounds (noun-noun nominals). On the basis of interpretability ratings, novel compounds were classified as being of either high or low interpretability. In a lexical decision task in which novel compounds functioned as nonwords, a significant interference effect was found for compounds of high interpretability. In a naming task, no differences were found between the two types of novel compounds, but lexicalized compounds resulted in shorter latencies than did novel compounds. Novel compounds were also shown to be interpreted under conditions unfavorable to morphological decomposition, suggesting that the interpretation process is beyond strategic control by the subject. Equal semantic priming effects were obtained for members of established semantic categories and nouns of highly interpretable compounds. Interpretative processes dealing with a limited set of basic semantic relations and analogy with lexicalized compounds are discussed.     

Boltzmann and Wittgenstein or How Pictures Became Linguistic

Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, namely, what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig Wittgenstein. This revised version was published online in June 2006 with corrections to the Cover Date.     

Weighted least squares fitting using ordinary least squares algorithms

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author.     

Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the three modes of a three-way array; the 3MFA model also uses a three-way core array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3MFA model the components are not uniquely determined, and it seems hard to choose among all possible solutions. A particularly interesting feature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and PARAFAC that share the good properties of the 3MFA model and the PARAFAC model: They fit (almost) as well as the 3MFA model, they are relatively simple and they have the same uniqueness properties as the PARAFAC model.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. Part of this research has been presented at the first conference on ThRee-way methods In Chemistry (TRIC), a meeting of Psychometrics and Chemometrics, Epe, The Netherlands, August 1993. The authors are obliged to Age Smilde for stimulating this research, and two anonymous reviewers for many helpful suggestions.     

Assessment Center Procedures: Cognitive Load During the Observation Phase

This study explores the traditional procedure of observing assessment center exercises while taking notes vs. an alternative procedure where assessors merely observe and postpone note‐taking until immediately after the exercise. The first procedure is considered to be cognitively demanding due to the requirement of simultaneous note‐taking and observing. Also, dual task processing (concurrent observing and note‐taking) is considered to be especially demanding for assessors without rating experience. The procedures are evaluated using a 2 × 2 design (with note‐taking/without note‐taking × experienced/inexperienced). Some 121 experienced and inexperienced assessors rated videotaped candidates, observing either with or without taking notes. Results showed that experienced assessors yield significantly higher differential accuracy than inexperienced assessors. We did not find an effect of observation procedure on accuracy, interrater reliability or halo. Implications for future research are described.