Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.Financial support by the Netherlands organization for scientific research (NWO) is gratefully acknowledged.     

Patient variable biases in clinical judgment: conceptual overview and methodological considerations

Specific conceptual factors are presented as having contributed to the negative findings of past psychotherapy bias research. Among these factors are the restrictive nature of both the definition of bias and the model of the biased clinician. A review of published studies of several patient variable biases (e.g., gender, race/ethnicity, and age) indicated that bias may best be defined in broader terms and that its occurrence may be more circumscribed than originally conceived. In addition, the lack of a theoretical perspective in this area of research is noted and the applicability of some social cognitive processes is discussed. Methodological factors are also considered, and recommendations for future research are offered.     

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.     

Reading long words embedded in sentences: informativeness of word halves affects eye movements

The possibility was explored that the informativeness of a specific region within a word can influence eye movements during reading. In Experiment 1, words containing identifying information either toward the beginning or toward the end were displayed asymmetrically around the point of fixation so that the reader was initially presented with either the informative or noninformative zone. Words were read with shorter summed initial fixation time when the reading was started from the informative zone. In Experiments 2 and 3, the target words were presented in sentences that were to be comprehended. More attention was given to the informative endings of words than to redundant endings. The latter were also skipped more often. The duration of the first fixation was not affected by information distribution within the word, whereas the second fixation duration was. The results of these experiments lend good support to the hypothesis of immediate lexical control over fixation behavior and to the notion of a convenient viewing position.     

Response to commentaries on “A neurobiological model for near-death experiences”

This work has received financial support from FONDECYT (Project 1111-88). The authors also acknowledge the helpful comments of Dr. Bruce Cassels.     

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.     

Lay conceptions of personality: Eliciting tiers of a scientific conception of personality

Two studies are reported which examine the availability of scientific propositions of personality in lay conceptions of personality. It is argued from a social constructivist perspective that models of personality must derive from and refer to lay conceptions of persons. Eysenck's trait-type model of introversion-extraversion, containing specific propositions about phenotypic and genotypic differences between extraverts and introverts, was utilized as the scientific model of personality and its availability in lay conceptions of personality was examined in two studies. In the first study, subjects were presented with a genotypic characterization of either an introvert or an extravert target person and asked to infer corresponding phenotypic differences. In the second study, the inference process was reversed with subjects being asked to infer genotypic characteristics of introverts versus extraverts on the basis of phenotypic target person desecrations of the two types. Results from both studies show a high degree of accuracy in subjects' inferences, suggesting that laypersons have well-formed conceptions about personality containing ‘higher-order’ psychogenetic propositions corresponding to Eysenck's trait-type model. The implications of the findings for theory construction are discussed.