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.     

The rank of reduced dispersion matrices

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.     

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.     

A simplification of a completeness proof of Guaspari and Solovay

The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R ^– are improved and the relationship between R and R ^– is clarified.     

Mechanical output about the ankle in countermovement jumps and jumps with extended knee

In this study the mechanical output (e.g., force, contraction velocity, instantaneous power) about the ankle was measured during a jump with and without occurrence of transportation of power and pre-stretch potentiation. To examine this, a model of the m. triceps surae was used. Eleven subjects performed a maximal one-legged countermovement jump (CMJ) and a maximal one-legged jump with extended knee (EKJ). Ground reaction forces, cinematographic data and electromyograms of m. triceps surae were recorded. The power output, defined as the product of moment and angular velocity, and work done about the ankle were higher during CMJ (1404 W, 130 J) than during EKJ (852 W, 76 J). The peak moments were the same during both jumps. The model of the m. triceps surae showed that the power delivered by m. triceps surae was higher during CMJ than during EKJ, as a result of catapult-action of m. gastrocnemius tendon. The difference in work done is explained, in addition to transportation of energy, by a greater contraction range of m. soleus during CMJ. There is no reason to assume that pre-stretch potentiation plays a role in the difference in mechanical output. The results show that the mechanical output of muscles in complex movements is strongly dependent on the dynamics of the movement, and not only on its contractile capacity.     

Convergence in the physical appearance of spouses

This study attempted to determine whether people who live with each other for a long period of time grow physically similar in their facial features. Photographs of couples when they were first married and 25 years later were judged for physical similarity and for the likelihood that they were married. The results showed that there is indeed an increase in apparent similarity after 25 years of cohabitation. Moreover, increase in resemblance was associated with greater reported marital happiness. Among the explanations of this phenomenon that were examined, one based on a theory of emotional efference emerged as promising. This theory proposes that emotional processes produce vascular changes that are, in part, regulated by facial musculature. The facial muscles are said to act as ligatures on veins and arteries, and they thereby are able to divert blood from, or direct blood to, the brain. An implication of the vascular theory of emotional efference is that habitual use of facial musculature may permanently affect the physical features of the face. The implication holds further that two people who live with each other for a longer period of time, by virtue of repeated empathic mimicry, would grow physically similar in their facial features. Kin resemblance, therefore, may not be simply a matter of common genes but also a matter of prolonged social contact.A. L.Dear A. L.: As far as physical appearance is concerned, likes seem to attract. Some experts feel that this resemblance may partly be explained by the fact that couples who've lived together for some time usually eat the same diet and share the same habits. The Joyce Brothers Column April 1985 This work was supported by Grant BNS-8505981 from the National Science Foundation. We wish to thank all those who offered their photographs for the purposes of this study, and Joseph R. Zajonc for his helpful suggestions.     

A controlled trial of cognitive-behavioural and behavioural treatment of anorexia nervosa

This study was undertaken to investigate whether a cognitive-behavioural treatment procedure was superior to a standard behavioural treatment, in the outpatient therapy of patients with anorexia nervosa. The two treatments were also compared with a control treatment procedure consisting of routine outpatient management. Each group consisted of eight subjects. All the groups showed some improvement, but the findings did not provide support for the prediction that cognitive-behavioural treatment, designed specifically to manipulate both attitudes and behaviour, was superior to the other types of treatment. The implications of the findings are considered.     

The farm crisis: An analysis of social psychological distress among North Carolina farm operators

Using data from a statewide survey of North Carolina farm operators collected during a period of economic and ecological crisis, the relationships between perceived social psychological distress, social support, and demographic, farm structure, and socioeconomic characteristics were analyzed. Younger operators showed higher distress levels, and age and social support interact so that social support lowered distress levels more for younger than for older operators. Results also showed that total family income has a curvilinear relationship with perceived distress: low and high income farm operators manifest higher levels of distress than middle income operators. By identifying the farm operators that show the highest levels of distress, the results have implications for policy intervention and farm crisis support programs.