Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR ² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR ² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.     

DISTINGUISHING BETWEEN EXTINCTION AND PUNISHMENT EFFECTS OF RESPONSE BLOCKING: A REPLICATION

Lerman and Iwata (1996) described a method for distinguishing between sensory extinction and punishment effects of response blocking on self-injurious behavior maintained independent of social contingencies. Results of their study suggested that blocking decreased the self-injurious hand mouthing of their participant via punishment. The current replication of these procedures with the self-injurious eye poking of a woman with developmental disabilities produced patterns of responding indicating that, for this participant, blocking functioned as an extinction procedure.     

Linear relations amongk sets of variables

A family of solutions for linear relations amongk sets of variables is proposed. It is shown how these solutions apply fork=2, and how they can be generalized from there tok3.The family of solutions depends on three independent choices: (i) to what extent a solution may be influenced by differences in variances of components within each set; (ii) to what extent the sets may be differentially weighted with respect to their contribution to the solution—including orthogonality constraints; (iii) whether or not individual sets of variables may be replaced by an orthogonal and unit normalized basis.Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted.     

Some symmetric,invariant measures of multivariate association

A distinction is drawn between redundancy measurement and the measurement of multivariate association for two sets of variables. Several measures of multivariate association between two sets of variables are examined. It is shown that all of these measures are generalizations of the (univariate) squared-multiple correlation; all are functions of the canonical correlations, and all are invariant under linear transformations of the original sets of variables. It is further shown that the measures can be considered to be symmetric and are strictly ordered for any two sets of observed variables. It is suggested that measures of multivariate relationship may be used to generalize the concept of test reliability to the case of vector random variables.     

THE LIMITS AND MOTIVATING POTENTIAL OF SENSORY STIMULI AS REINFORCERS FOR AUTISTIC CHILDREN

This study investigated the reinforcing properties, limits, and motivating potentials of sensory stimuli with autistic children. In the first phase of the study, four intellectually retarded autistic children were exposed to three different types of sensory stimulation (vibration, music, and strobe light) as well as edible and social reinforcers for ten-second intervals contingent upon six simple bar pressing responses. In the second phase, the same events were used as reinforcers for correct responses in learning object labels. The results indicated that: (a) sensory stimuli can be used effectively as reinforcers to maintain high, durable rates of responding in a simple pressing task; (b) ranked preferences for sensory stimuli revealed a unique configuration of responding for each child; and (c) sensory stimuli have motivating potentials comparable to those of the traditional food and social reinforcers even when training receptive language tasks.     

Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

A comparison of a modified sequential oral sensory approach to an applied behavior‐analytic approach in the treatment of food selectivity in children with autism spectrum disorder

Treatments of pediatric feeding disorders based on applied behavior analysis (ABA) have the most empirical support in the research literature (Volkert & Piazza, 2012); however, professionals often recommend, and caregivers often use, treatments that have limited empirical support. In the current investigation, we compared a modified sequential oral sensory approach (M‐SOS; Benson, Parke, Gannon, & Muñoz, 2013) to an ABA approach for the treatment of the food selectivity of 6 children with autism. We randomly assigned 3 children to ABA and 3 children to M‐SOS and compared the effects of treatment in a multiple baseline design across novel, healthy target foods. We used a multielement design to assess treatment generalization. Consumption of target foods increased for children who received ABA, but not for children who received M‐SOS. We subsequently implemented ABA with the children for whom M‐SOS was not effective and observed a potential treatment generalization effect during ABA when M‐SOS preceded ABA.     

Against the Additive View of Imagination

According to the additive view of sensory imagination, mental imagery often involves two elements. There is an image-like element, which gives the experiences qualitative phenomenal character akin to that of perception. There is also a non-image element, consisting of something like suppositions about the image's object. This accounts for extra-sensory features of imagined objects and situations: for example, it determines whether an image of a grey horse is an image of Desert Orchid, or of some other grey horse. The view promises to give a simple and intuitive explanation of some puzzling features of imagination, and, further, to illuminate imagination's relation to modal knowledge. I contend that the additive view does not fulfil these two promises. The explanation of how images come to be determinate is redundant: the content constituting the indeterminate mental images on which the view relies is sufficient to deliver determinate images too, so the extra resources offered by the view are not required. When applied to modal epistemology, the view either delivers implausible results or offers no distinctive insight. Since the view is sold on its explanatory merits, and since these are dubious, the additive view should be rejected.