Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

Using item-specific instructional information in achievement modeling

The problem of detecting instructional sensitivity (item basis) in test items is considered. An illustration is given which shows that for tests with many biased items, traditional item bias detection schemes give a very poor assessment of bias. A new method is proposed instead. This method extends item response theory (IRT) by including item-specific auxiliary measurement information related to opportunity-to-learn. Item-specific variation in measurement relations across students with varying opportunity-to-learn is allowed for.This paper was presented at the 1987 AERA meeting in Washington, DC. This research was supported by grant OERI-G-86-003 from the Office of Educational Research and Improvement, Department of Education. The author thanks Michael Hollis and Chih-fen Kao for valuable research assistance, and appreciates valuable comments made by an anonymous reviewer.     

Social anxiety and fear of bodily sensations in panic disorder and agoraphobia: A matched comparison

This study tests the hypothesis that social anxiety and fear of bodily sensations are associated with the development of agoraphobic avoidance behavior in panic disorder patients. Twenty patients with panic disorder were compared to 20 patients with panic disorder with agoraphobia, matched by sex and duration of disorder. The two groups did not differ on measures of fear and frequency of assertive social responses. However, the agoraphobics scored higher on measures of interpersonal sensitivity, depression, feelings of inadequacy, and hostility. They also reported higher fear of bodily sensations. Although definitive conclusions need to be postponed until prospective studies have been conducted, there is evidence suggesting that the development of agoraphobia in panic patients is associated with hypersensitivity to bodily sensations and interpersonal situations.This research was supported by Grant 560-268-009 of the Dutch Organization for Scientific Research.     

Resistance revisited

It was a coincidence that I was asked to talk about resistance at Ground Rounds at the University of Texas, Department of Psychiatry, on the tenth anniversary of mailing the first version of Death of Resistance to a journal in 1979. Although the paper was subsequently rejected 17 times and revised six times, it was eventually published inFamily Process (de Shazer, 1984). I still insist that the concept of resistance was a bad idea for therapists to have in their heads.This paper was presented April 14, 1989, at Ground Rounds, University of Texas, Southwest Medical Center, Department of Psychiatry, Dallas, Texas.     

Factor structure in groups selected on observed scores

A new method is proposed for estimating factor means and factor covariances in a group of individuals selected on their observed scores. The selection variable is, for example, the total score on an admissions test. Given a factor model for the test items based on the group of test takers, we may be interested in the factor structure for those in the top quartile. The differences in factor means and covariances between this selected group and the full group gives useful information both on successful test performance and on test validity. The new method draws on the classic Pearson-Lawley selection formulas. It avoids the fallacy of factor analysis on the selected group, which would lead to incorrect estimates. The new method is applied to a simple factor structure model for the GMAT test. Although the majority of the GMAT items test verbal skills, it is found that a quantitative factor shows the greatest change in moving from average to top quartile test takers.     

Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.     

Early adolescent egocentrism: a review of six articles

This paper reviews six articles which appear to be representative of the past fifteen years during which researchers have focused on early adolescent egocentrism. Each article is described in chronological order and compared to research findings suggested by the other articles. Although the researchers have suggested some interesting associations, there is a lack of consistency among their findings. The author indicates methodological problems and questions for further research which arise from the reviewed articles.     

Sexual experience and preference for males or females in the female rat

The influence of sexual experience on preference behavior was investigated in adult female rats. In the first experiment, preference behavior for sexually active males versus estrous females was investigated in female rats who were experienced with mounting behavior. Preference of these mount experienced females was compared to preference of females who were naive in this respect. Mount experience with estrous females induced a female-directed preference in ovariectomized female rats, irrespective of whether the females were treated with OIL or with testosterone-propionate (500 micrograms TP, injected once 48 h prior to testing). Sexually naive, OIL-treated females did not show a preference for males or females, but TP induced a preference for a male. Individual differences in mount frequency were not correlated with preference behavior. In the second experiment, the influence of experience with feminine sexual responses on preference behavior was investigated. OIL-treated and TP-treated females oriented equally toward males and females when they had been given the opportunity to copulate with males prior to the preference tests. The results strongly suggest that prior sexual experience is an important determinant of preference behavior. The female's behavior during sexual interactions was, however, not predictive of later preference.