Range restrictions for product-moment correlation matrices

It is well-known that for a trivariate distribution if two correlations are fixed the remaining one is constrained. Indeed, if one correlation is fixed, then the remaining two are constrained. Both results are extended to the case of a multivariate distribution. The results are applied to some special patterned matrices.     

The rowwise correlation between two proximity matrices and the partial rowwise correlation

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel'sZ. It is shown that the rowwise matrix correlation coefficient between two matricesX andY is the partial correlation between the entries ofX andY controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.The author wishes to thank the Editor, two referees, Jan van Hooff, and Ruud Derix for their useful comments, and E. J. Dietz for a copy of the algorithm of the Mantel permutation test.     

The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

MODIFICATION OF COMBINED MIGRAINE-MUSCLE CONTRACTION HEADACHES USING BVP AND EMG FEEDBACK

The effect of blood volume pulse (BVP) and frontalis muscle action potential (EMG) feedback on control of vasoconstriction of the temporal artery and frontalis muscle activity in combined migraine-muscle tension subjects was investigated in a multiple baseline design (across subjects and responses). The data indicated: (a) both subjects obtained an ability to control BVP during BVP feedback and EMG during EMG feedback; (b) there were decreases in frequency of migraine headaches during BVP feedback and decreases in muscle contraction headaches during EMG feedback. The results of this study supported the theoretical explanation of two pain mechanisms involved in combined muscle contraction-migraine headaches as well as the effectiveness of biofeedback procedures that target directly the specific pain mechanism in the elimination of the two types of head pain.     

A note on the factor analysis of partial covariance matrices

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.     

Discrimination training, partial reinforcement, and increases in intertrial interval all reduce response speed in a continuously reinforced key-pecking task

Pigeons were trained in a discrete-trial task in which a response to the center key obtained illumination of a side key and a single response to the side key terminated a trial with either reinforcement or nonreinforcement. Center-key speeds (i.e., reciprocals of latencies) declined with increases in intertrial interval, and it is argued that this effect is related to a decreased likelihood as intertrial interval increases that birds will be near the key at trial onset. Side-key speeds on trials with reinforcement decreased both with increases in intertrial interval and with shifts from continuous reinforcement to either a discrimination or a partial-reinforcement condition. The effects on side-key speeds are compared with effects observed in alley-running tasks using rats, and an interpretation in terms of frustration theory is offered for the results obtained in both types of task.     

PLS model building: A multivariate approach to personality test data

The aim of this study was to demonstrate how personality test data can be plotted with a multivariate method known as Partial Least Squares of Latent Structures (PLS). The basic methodology behind PLS modeling is presented and the example demonstrates how a PLS model of personality test data can be used for diagnostic prediction. Principles for validating the models are also presented. The conclusion is that PLS modeling appears to be a powerful method for extracting clinically relevant information from complex personality test data matrixes. It could be used as a complement to more hard modeling methods in the process of examining a new area of interest.     

Balance Performance During Perturbed Standing Is Not Associated With Muscle Strength and Power in Young Adults

The authors investigate the ways in which varied postural responses to translating platform perturbations are associated with the variables of strength and power. Twenty-four physically active and 27 sedentary young adults were exposed to a set of postural perturbations at varied velocities (10 and 20 cm/s) and the respective accelerations (6.4 and 6.9 m/s²), constant distance (6 cm), and 4 directions of platform motion (forward, backward, left-lateral, and right-lateral). They also performed maximum voluntary isometric contraction (MVC) and chair rising/chair jumping tests. The analysis of variance revealed significant interaction effect for peak center of pressure displacement, direction by velocity: F_3,129 = 24.43, p = .002; and direction by acceleration: F_3,129 = 34.18, p = .001. There were no significant correlations between peak center of pressure displacements and peak force and peak rate of force development measured during MVC in either standing (r = .27–57) or sitting positions (r = .12–51) and peak power during chair jumping (r = .47–.59) in all participants. As such, only a small proportion of variance was explained (9–39%, 3–23%, and 23–41%, respectively). In conclusion, interaction effects indicate that the composition of stimuli strongly influences compensatory responses and this effect is more pronounced in sedentary than in physically active young adults. Nevertheless, the dynamic balance is not associated with muscle strength and power in either group.     

Semi-automated Rasch analysis using in-plus-out-of-questionnaire log likelihood

Rasch analysis is a popular statistical tool for developing and validating instruments that aim to measure human performance, attitudes and perceptions. Despite the availability of various software packages, constructing a good instrument based on Rasch analysis is still considered to be a complex, labour-intensive task, requiring human expertise and rather subjective judgements along the way. In this paper we propose a semi-automated method for Rasch analysis based on first principles that reduces the need for human input. To this end, we introduce a novel criterion, called in-plus-out-of-questionnaire log likelihood (IPOQ-LL). On artificial data sets, we confirm that optimization of IPOQ-LL leads to the desired behaviour in the case of multi-dimensional and inhomogeneous surveys. On three publicly available real-world data sets, our method leads to instruments that are, for all practical purposes, indistinguishable from those obtained by Rasch analysis experts through a manual procedure.     

Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction

On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within the framework of a logic based on inclusion and unrestricted abstraction, without any form of extensionality. This revised version was published online in June 2006 with corrections to the Cover Date.