Fitting longitudinal reduced-rank regression models by alternating least squares

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.Financial support by the Institute for Traffic Safety Research (SWOV) in Leidschendam, The Netherlands is gratefully acknowledged.     

A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.     

Scene perception: Detecting and judging objects undergoing relational violations

Five classes of relations between an object and its setting can characterize the organization of objects into real-world scenes. The relations are (1) Interposition (objects interrupt their background), (2) Support (objects tend to rest on surfaces), (3) Probability (objects tend to be found in some scenes but not others), (4) Position (given an object is probable in a scene, it often is found in some positions and not others), and (5) familiar Size (objects have a limited set of size relations with other objects). In two experiments subjects viewed brief (150 msec) presentations of slides of scenes in which an object in a cued location in the scene was either in a normal relation to its background or violated from one to three of the relations. Such objects appear to (1) have the background pass through them, (2) float in air, (3) be unlikely in that particular scene, (4) be in an inappropriate position, and (5) be too large or too small relative to the other objects in the scene. In Experiment I, subjects attempted to determine whether the cued object corresponded to a target object which had been specified in advance by name. With the exception of the Interposition violation, violation costs were incurred in that the detection of objects undergoing violations was less accurate and slower than when those same objects were in normal relations to their setting. However, the detection of objects in normal relations to their setting (innocent bystanders) was unaffected by the presence of another object undergoing a violation in that same setting. This indicates that the violation costs were incurred not because of an unsuccessful elicitation of a frame or schema for the scene but because properly formed frames interfered with (or did not facilitate) the perceptibility of objects undergoing violations. As the number of violations increased, target detectability generally decreased. Thus, the relations were accessed from the results of a single fixation and were available sufficiently early during the time course of scene perception to affect the perception of the objects in the scene. Contrary to expectations from a bottom-up account of scene perception, violations of the pervasive physical relations of Support and Interposition were not more disruptive on object detection than the semantic violations of Probability, Position and Size. These are termed semantic because they require access to the referential meaning of the object. In Experiment II, subjects attempted to detect the presence of the violations themselves. Violations of the semantic relations were detected more accurately than violations of Interposition and at least as accurately as violations of Support. As the number of violations increased, the detectability of the incongruities between an object and its setting increased. These results provide converging evidence that semantic relations can be accessed from the results of a single fixation. In both experiments information about Position was accessed at least as quickly as information on Probability. Thus in Experiment I, the interference that resulted from placing a fire hydrant in a kitchen was not greater than the interference from placing it on top of a mail ? in a street scene. Similarly, violations of Probability in Experiment II were not more detectable than violations of Position. Thus, the semantic relations which were accessed included information about the detailed interactions among the objects—information which is more specific than what can be inferred from the general setting. Access to the semantic relations among the entities in a scene is not deferred until the completion of spatial and depth processing and object identification. Instead, an object's semantic relations are accessed simultaneously with its physical relations as well as with its own identification.     

Perception of autonomic reactions and actual heart rate in phobic patients

The relationship between perceived physiological arousal and actual heart-rate reactions was studied in two behavioral test situations. The subjects were 70 phobic patients (34 social phobics and 36 claustrophobics) who were given the general form of the Autonomic Perception Questionnaire about 1 month before the respective behavioral test and the specific form immediately after the test. The results showed significant correlations between APQ and actual heart rate for the social phobics, while the picture was more complicated for the claustrophobics. The implications of these results are discussed.This research was supported by Grant 05452 from the Swedish Medical Research Council.     

The influence of relative frequencies of pure and mixed stimuli on mixture suppression in taste

In experiments on saltiness suppression in NaCL-sucrose mixtures, the amount of suppression depends not only on the suppressing sucrose component in the mixture, but also on the relative frequencies of pure NaCL stimuli and mixed stimuli in the series. The observed variation of mixture suppression as a function of these frequencies can be explained by Helson’s adaptation level theory.     

A study of orientation errors in response to Kohs-type figures(1)

In order to elucidate the nature of the orientation errors encountered when subjects are required to reproduce Kohs-type figures, subjects drawn from a culture where such errors are reported to be relatively common were required to reproduce orientation of simple figures. It was found that the responses made in the case of square figures showed a definite drift towards a “stable” orientation; the drift observed in the case of circular stimuli was too weak to permit an unambiguous interpretation. The relevance of these data to previous data on cross-cultural differences in responses to Kohs-type stimuli is briefly examined.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.