A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Disentangling Type A behavior: The roles of ambition,insensitivity, and anxiety

This study identified stable components of Type A behavior as usually defined, and examined their relationships with more traditional psychological constructs. Overall scores on the most popular Type A measure (a version of the Jenkins Activity Survey) were moderately associated with ambition but largely unrelated to measures of adjustment. An item analysis yielded subcomponents of Drivenness and Involvement. Drivenness was unrelated to ambition, but was positively related to anxiety and negatively related to interpersonal perceptiveness. Involvement was positively related to ambition and to interpersonal competence. It is suggested that the Jenkins Activity Survey measures a heterogeneous mixture of constructive commitment and self-defeating responses that clouds its psychological interpretation.     

Two factors of restraint: concern for dieting and weight fluctuation

Factor analysis of the Restraint Scale produced two replicated factors: Concern for Dieting and Weight Fluctuation. Concern for Dieting reflects heightened attention to and emotional association with eating. Weight Fluctuation reflects extent of previously-experienced weight gain and loss. Weight Fluctuation was more highly positively correlated with indices of overweight status than was Concern for Dieting. Concern for Dieting was positively correlated with Public Self-Consciousness and Social Anxiety while Weight Fluctuation was not. Both versions of Restraint were weakly and inversely correlated with Body Image, although this relationship was mediated by degree of overweight status. The findings indicate that the two factors are sufficiently distinct to preclude combination into a single scale. Furthermore. Weight Fluctuation appears to be the more promising subscale for future research.     

Cognitive deficits in compulsive checkers: An exploratory study

Compulsive-checking behavior can be conceptualized as resulting, in part, from a memory failure. In order to determine if memory difficulties are associated with compulsive checking, the performance of college-student checkers were compared with the performance of non-checkers on a number of cognitive tasks hypothesized to be relevant to understanding checking behavior. Using the Checking and Cleaning subscales of the Maudsley Obsessional-Compulsive Inventory, four groups of subjects were identified: (1) Cleaning Checkers (N = 13); (2) Noncleaning Checkers (N = 13); (3) Cleaning Noncheckers (N = 13); and (4) Noncleaning Noncheckers (N = 15). It was hypothesized that the cognitive deficits studied would characterize individuals with cheeking compulsions, but not persons with non-checking compulsions (i.e. Cleaning Noncheckers) or normal controls (i.e. Noncleaning Noncheckers). Compulsive checkers were found to have a poorer memory for prior actions than non-checkers and were also found to underestimate their ability at distinguishing memories of real and imagined events, a process referred to as reality monitoring. Both of these deficits were specific to compulsive checkers and can be viewed as contributing to the likelihood that an individual will engage in checking behavior. If an individual has difficulty in recalling whether an intended action has been executed, they may be inclined to engage in checking behavior to insure the intended action is carried out. Similarly, a tendency to underestimate reality-monitoring ability could result in increased checking behavior as the individual attempts to reduce his/her uncertainty over whether a previous behavior actually occurred or merely was thought to occur. It is concluded that the study of cognitive deficits in compulsive checking is a potentially fruitful avenue for further inquiry.     

Anxiety induced by cardiac perceptions in patients with panic attacks: a field study

In panic disorder bodily sensations appear to play an important role as a trigger for anxiety. In our psychophysiological model of panic attacks we postulate the following vicious circle: individuals with panic attacks perceive even quite small increases in heart rate and interpret these changes as being catastrophic. This elicits anxiety and a further increase in heart rate. To evaluate this model we conducted a field study of 28 subjects with panic attacks and 20 healthy controls. A 24 hr ambulatory ECG was recorded and the subjects were instructed to report any cardiac perceptions during this period and to rate the anxiety elicited by these perceptions. The incidence of cardiac perceptions was about the same in both groups, but only subjects with panic attacks reported anxiety associated with such perceptions. Analysis of the ECGs revealed that in both groups heart rate accelerations preceded cardiac perceptions. Following cardiac perceptions, the healthy controls showed a heart rate deceleration, whereas the subjects with panic attacks had a further acceleration. This heart rate increase after cardiac perceptions was positively related to the level of anxiety elicited by the perceptions. These results provide clear evidence in support of the vicious circle model of panic attacks.     

The rights of research assistants and the rhetoric of political suppression: Morton Grodzins and the University of California Japanese-American Evacuation and Resettlement Study

This case study of an inter-university controversy over the publication of research from an interdisciplinary social science project on the forced migration and long-term internment of West Coast Japanese-Americans during World War II shows some of the difficulties of maintaining ownership of research materials. In this particular instance the junior employee was able to override his seniors' demand for control of the dissemination of research results by playing on the concerns about even appearing to suppress work for political reasons. The paper discusses conflicting norms of science and rhetorics of justification ranging from proprietary self-interest through "good science" to "the national interest" and onto "the needs of a free society."     

Dilthey''s narrative model of human development: Necessary reconsiderations after the philosophical hermeneutics of Heidegger and Gadamer

Paper delivered at theEighth International Human Science Research Conference at Aarhus University (Denmark), 18–22 August 1989.     

Maximum marginal likelihood estimation for semiparametric item analysis

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.IRCAMThe research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).