Some uniqueness results for PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2. The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting major improvements in the presentation.     

Objectively reliable subjective probabilities

Subjective Bayesians typically find the following objection difficult to answer: some joint probability measures lead to intuitively irrational inductive behavior, even in the long run. Yet well-motivated ways to restrict the set of reasonable prior joint measures have not been forthcoming. In this paper I propose a way to restrict the set of prior joint probability measures in particular inductive settings. My proposal is the following: where there exists some successful inductive method for getting to the truth in some situation, we ought to employ a (joint) probability measure that is inductively successful in that situation, if such a measure exists. In order to do show that the restriction is possible to meet in a broad class of cases, I prove a Bayesian Completeness Theorem, which says that for any solvable inductive problem of a certain broad type, there exist probability measures that a Bayesian could use to solve the problem. I then briefly compare the merits of my proposal with two other well-known proposals for constraining the class of admissible subjective probability measures, the leave the door ajar condition and the maximize entropy condition.The author owes special thanks to Kevin Kelly, for a number of helpful ideas for the proof of the Bayesian Completeness Theorem, as well as other aspects of the paper. Thanks also to Clark Glymour for some helpful suggestions for improvement of an earlier draft. Part of the work leading to this paper was funded by a Summer Research Grant from the University Research Institute of the University of Texas at Austin.     

Agency and obligation

The purpose of this paper is to explore a new deontic operator for representing what an agent ought to do; the operator is cast against the background of a modal treatment of action developed by Nuel Belnap and Michael Perloff, which itself relies on Arthur Prior's indeterministic tense logic. The analysis developed here of what an agent ought to do is based on a dominance ordering adapted from the decision theoretic study of choice under uncertainty to the present account of action. It is shown that this analysis gives rise to a normal deontic operator, and that the result is superior to an analysis that identifies what an agent ought to do with what it ought to be that the agent does.     

Dispositionai Optimism as a Protective Factor in Resisting HIV Exposure in Sexually Active Inner-City Minority Adolescents1

Recent investigations have explored dispositional optimism as a determinant of various health-related behaviors, though such research has been infrequently conducted in populations where pessimism would be expected to be prevalent. The present study examines optimism and unsafe sexual behavior in 230 sexually active inner-city minority adolescents. Findings suggest that dispositional optimism is a protective factor regarding adolescents' intentions to avoid engaging in unsafe sex. Further, the benefits of optimism appear to be explained by those who are more optimistic having higher levels of perceived condom use self-efficacy and stronger negative expectancies toward unsafe sex. Future interventions may need to address optimism in concert with behavioral-specific determinants to increase the probability of reducing unsafe sexual behavior in high-risk populations.     

Predicting Adolescents' Initiation of Intercourse and Contraceptive Use

This paper examines whether variables consistent with problem behavior theory predict grade of onset of first intercourse and adoption of effective contraception. A total sample of 3,419 Wisconsin adolescents in Grades 7, 9, and 11 participated in a survey of health-related behaviors administered 3 times across a 6-year period. The sample is 87% White. Multiple regression methods generated different models for onset of sexual intercourse vs. contraceptive adoption. Consistent with problem behavior theory, sexual onset is predicted by the adolescent's behavioral system, perceived peer substance use/abuse, importance of friends, and extent to which the adolescent felt harried and believed it was okay to break laws. Contraceptive adoption is predicted by family structure, socioeconomic variables, and self-esteem. Age and gender model differences emerged.     

ASSESSMENT AND TREATMENT OF DESTRUCTIVE BEHAVIOR MAINTAINED BY STEREOTYPIC OBJECT MANIPULATION

In the current investigation, 2 participants with mental retardation displayed property destruction and stereotypy, and both responses involved the same materials (e.g., breaking and tapping plastic objects). Three experiments were conducted (a) to indirectly assess the functions of these two responses, (b) to determine their relation to one another, and (c) to develop a treatment to reduce the more serious behavior, property destruction. In Experiment 1, previously destroyed materials were either present or absent, and their presence reduced property destruction but not stereotypy. In Experiment 2, matched toys (ones that produced sensory stimulation similar to stereotypy) were either present or absent, or were replaced by unmatched toys (for 1 participant). Matched toys produced large reductions and unmatched toys produced small reductions in property destruction and stereotypy. In Experiment 3, attempts to pick up undestroyed objects were either blocked or not blocked while matched toys were continuously available. Response blocking reduced property destruction (and attempts), prevented stereotypy, and increased manipulation of matched toys. These results suggest that the two aberrant responses formed a chain (e.g., breaking and then tapping the object), which was maintained by the sensory consequences (e.g., auditory stimulation) of the terminal response, and that previously destroyed material or matched toys made the initial response (property destruction) unnecessary.     

Promoting Resilience in At-Risk Children

Intervening effectively with youths at risk from early deprivation, family dysfunction, poverty, abuse, and other factors is a major concern for educational and social service policymakers. Current research suggests that a majority of at-risk youths do not experience drastic outcomes, but many exhibit protective factors that buffer them from negative consequences. Longitudinal studies from Hawaii, the continental United States, and Great Britain have identified several personality, familial, and environmental variables that promote resiliency in youths at risk. This article discusses these variables and provides counselors with an assessment technique and strategies to promote a salutogenesis perspective.     

Interpersonal conflict in group therapy: An object relations perspective

The aim of this paper is to demonstrate how object relations theory can be used to understand and regulate interpersonal conflict in group psychotherapy. Such concepts as projective identification, intersubjectivity and the analytic third are used to describe how conflict emerges in group psychotherapy and how it can be worked through. Case material is also provided to illustrate concepts and techniques in promoting a group's transition from a paranoid/schizoid to a depressive position. Positive aspects of the concept of projective identification are discussed including its use as a form of communication, a method of reducing anxiety and reintegrating previously dangerous and threatening aspects of the self.The paper was funded by Evan F. Lilly Memorial Trust Grant PV 13,067.