ON THE NONCENTRAL DISTRIBUTION OF A RANDOM MATRIX USEFUL IN CLASSIFICATION THEORY

To prove the optimality properties of the maximum likelihood (and also minimum distance) discriminant rule Rogers (1980, p. 98) embeds the maximum likelihood discriminant function in a Cauchy-Schwartz inequality. This embedding procedure of Rogers (1980) may be used to derive a new distribution for Anderson's (1958) classification statistic.     

Commentary: answers and questions in the sociology of mental health

This commentary speaks to several issues that arise from the papers in this special issue. Two articles--Kessler (2002) and Mirowsky and Ross (2002)--focus on a major measurement issue: dimensional versus diagnostic-type assessments. One topic requires greater attention: the correspondence of these measures with the underlying states they supposedly measure--constructs in the psychometric tradition and empirically defined illnesses in the medical or psychiatric tradition. Conclusions about the nature of these unobserved states remain tentative at this time. Three articles--Keyes (2002), Schwartz (2002), and Umberson, Williams, and Anderson (2002)--address the expansion of mental health outcomes. The existing reliance on emotional distress is problematic for sociological research because a single disorder is not a good proxy for estimates of the overall mental health consequences of social arrangements. Although these papers present diverse and sometimes conflicting perspectives, collectively they demonstrate that no one approach to outcomes is best for all research questions.     

The expected personality characteristics of alcohol-dependent individuals

The Big Five personality factors were used as a framework for examining the expected personality characteristics of individuals who are alcohol-dependent. In an experimental study, participants used a measure of the Big Five personality factors to rate two individuals, each described with either signs of alcohol dependence or not. The ratings of the participants showed that they expected the alcohol-dependent versions of both individuals to be less agreeable and less conscientious. The participants expected the alcohol-dependent college student to be more extraverted and the alcohol-dependent lawyer-father to be more neurotic. The expected personality characteristics of the alcohol-dependent versions of the two described persons were very similar to the actual personality characteristics of alcohol-dependent individuals. The results were consistent with prior findings regarding narrow-band personality traits related to the Big Five. The results help explain prior findings about the social handicap of problem drinking with regard to making friends, dating, marriage, and working. The findings have potential use in alcohol-problem prevention and treatment.     

Characteristics of effective providers of marital and family therapy in rural mental health settings

Characteristics of effective providers of marital and family therapy (MFT) in rural mental health settings were investigated. The survey sample included 74 members of the National Association for Rural Mental Health who, through a modified Delphi process, created a composite picture of effective MFT providers. The findings yielded six major rank-ordered characteristics of effective MFT providers in rural mental health settings, with effective skills in MFT ranked first. Rural community understanding, appreciation and participation ranked second. Specific competencies contributing to each major characteristic were also identified and are discussed. Recommendations for use of this information are provided.     

Quality improvement in patient distribution at a major university student health center

Healthcare in a major university setting poses unusual challenges and great opportunities. Two traditionally challenging areas in patient distribution are the initial intake of allergy/immunization patients and the triage of outpatients in the general medical clinic. The authors describe the use of the FOCUS-PDCA quality improvement (QI) problem-solving process for each situation. After identifying major problems, the health center established cross-functional teams of experts representing the allergy/immunization and general medical clinics. The teams analyzed the problems with a flow chart and undertook studies to further elucidate causes and potential solutions. They listed potential solutions in order of priority and submitted them to the student health center director for review and initiation. Each team then used the PDCA (plan-do-check-act) cycle to put approved solutions into effect. Permanent improvements made in each area resulted in a more effective and efficient patient distribution system, favorable staff comment, and greater patient satisfaction.     

Calculating the density and distribution function for the singly and doubly noncentral F

Simple, closed form saddlepoint approximations for the distribution and density of the singly and doubly noncentral F distributions are presented. Their overwhelming accuracy is demonstrated numerically using a variety of parameter values. The approximations are shown to be uniform in the right tail and the associated limitating relative error is derived. Difficulties associated with some algorithms used for exact computation of the singly noncentral F are noted.     

Perfect simulation for correlated Poisson random variables conditioned to be positive

In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thönnes (Pattern Recognition 32(9): 1569–1586, 1999), this special case was treated in a more complicated way. The method is applied to several simple examples where exact calculations can be made, so as to check correctness of the program using ²-tests, and some small-scale experiments are carried out to explore the behaviour of the conditioned Boolean model.