Visual perception of surface curvature: psychophysics of curvature detection induced by motion parallax

The continuous approach to optic-flow processing shows that the curvature of a moving surface is related to a second spatial derivative of the velocity field, the spin variation (Droulez & Cornilleau-Pérès, 1989). With this approach as a theoretical framework, visual sensitivity to the curvature of a cylinder in motion was measured using a task of discrimination between cylindrical and planar patches. The results confirm the predictions suggested by the theory: (1) Sensitivity to curvature was always greater when the cylinder axis and the frontal translation were parallel than when they were orthogonal. The ratio of curvature detection thresholds in the two cases was between 1.3 and 2.5; the value predicted from the spin variation theory is about 2. (2) Sensitivity to curvature increased strongly with the velocity of the motion but was only weakly affected by its amplitude and the duration of viewing for the range of values used in our experiments.     

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.     

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.     

STRATÉGIES COGNITIVES ET PROCESSUS D'AUTORÉGULATION CHEZ DES FAMILLES EN SITUATION DE RÉSOLUTION DE PROBLÈMES LOGIQUES*

The family is a fundamental learning environment for many basic skills such as the ability to solve everyday domestic problems. A lack of competence in this type of problem solving would expose the individual to more frustration and possibly create the conditions for greater aggression. Forty-two low SES families, each including an aggressive boy, were invited to the laboratory for a problem-solving session on two occasions, at an interval of two years. Subjects were asked to find four preset combinations of colours by systematic permutations of four colours using a computer. Three types of cognitive performance were examined: resolution strategies, autoregulation strategies and the success rate in finding the solution. Results showed that most of the families were consistent in their use of a non-systematic strategy. Although some improvement in planning is observed during the second testing, no other improvement in autoregulation strategies was observed. In general, families had a better rate of success in finding the solution in the second session. The low cognitive level of these families and its stability are discussed. Étant donné que la famille constitue un terrain privilégié d'apprentissage, l'aggressivité comportementale de certains enfants pourrait résider dans le peu d'opportunités offertes par leur famille d'apprendre à affronter les problèmes de la vie quotidienne d'une manière réfléchie. Quarante-deux familles de milieu socio-économique faible, dont un des enfants est à risque d'inadaptation sociale et dont les parents sont peu scolarisés, ont à résoudre un problème nécessitant l'intelligence logique et ce, à deux ans d'intervalle (T-1 et T-2). La tâche consite à résoudre un problème de permutations à quatre éléments et se présente sous la forme d'un jeu d'ordinateur. Le fonctionnement cognitif est examiné selon trois dimensions: les stratégies cognitivcs de résolution, les stratégies d'autorégulation exercées, sur la démarche cognitive et l'issue de la démarche cognitive. L'examen des stratégies cognitives révèle que la majorité des familles utilisent une approche non stratégique et que cette approche est maintenue aussi bien à l'intérieur d'une séance donnée que d'une séance à l'autre. Exception faite de l'amélioration relevée à la séance 2 quant au contrôle exercé par les familles sur le déroulement de leur démarche cognitive, aucun changement n'émerge sur les autres critères de l'autorégulation. Finalement, les familles obtiennent une meilleure performance à la deuxième séance. La discussion porte sur la relative stabilité du niveau de fonctionnement cognitif des familles ainsi que sur la pauvreté apparente de leur répertoire de schèmes.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.