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.     

Improved bounds for optimal intervals in weakly constrained regression problems

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.     

Deontic database constraints,violation and recovery

The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (hard) and deontic (soft) constraints.Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this logic. The limitations of the proposed logic and possible modifications and extensions of it are analysed.     

Postural determinants of frontal-position advantage in listening to speech

Previous work has shown that when a subject is seated with body, head, and eyes oriented in the same direction, speech coming from the front is better perceived than speech coming from other directions. The question asked was which segments of the body are critical in determining the advantage of the frontal position. It was found that the effect does not depend exclusively on the orientation of the head relative to the source, since the advantage is reduced not only when the head is deviated laterally towards a competing source, but also when the gaze or the trunk and the limbs are deviated in that direction. Frontal position advantage is thus not a purely acoustical or auditory phenomenon, but depends, at least partly, on interactions at deeper levels.     

A general solution to Mosier's oblique procrustes problem

Browne provided a method for finding a solution to the normal equations derived by Mosier for rotating a factor matrix to a best least squares fit with a specified structure. Cramer showed that Browne's solution is not always valid, and proposed a modified algorithm. Both Browne and Cramer assumed the factor matrix to be of full rank. In this paper a general solution is derived, which takes care of rank deficient factor matrices as well. A new algorithm is offered.     

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.     

Peer Nomination Inventory of Depression: Characteristics in a Spanish sample

The Peer Nomination Inventory of Depression (PNID) was answered by 1,121 children from Barcelona in the fourth year of grammar school and by their teachers (n=36) to analyze this questionnaire in a Spanish sample. The results indicated (1) high internal consistency; (2) discriminative power between depressed and nondepressed; (3) low concurrent validity; (4) convergent and discriminant validity; (5) a two-factor structure; and (6) that two discriminant functions could differentiate between depressed, dysthymic, and nondepressed subjects. The teacher's responses showed (1) moderate internal consistency; (2) discriminative power between depressed and nondepressed groups; (3) moderate concurrent validity; (4) and that two discriminant functions could differentiate between the diagnostic groups. The importance of the information given by the teacher to help detect severe depressive problems was pointed out.