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.     

Binary programming and test design

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are presented. Within the same framework, it is also possible to formulate the problem of individualized testing.I would like to thank my colleagues N. Veldhuijzen, H. Verstralen and M. Zwarts for their suggestions and comments. Furthermore, I would like to thank Professor W. van der Linden, Department of Educational Measurement and Data Analysis, Technological University Twente, for offering facilities at his department; Ellen Timminga of the same department and S. Baas, department of Operational Research at the same University for their efforts in linear programming.     

Optimal sequential designs for on-line item estimation

Replenishing item pools for on-line ability testing requires innovative and efficient data collection designs. By generating localD-optimal designs for selecting individual examinees, and consistently estimating item parameters in the presence of error in the design points, sequential procedures are efficient for on-line item calibration. The estimating error in the on-line ability values is accounted for with an item parameter estimate studied by Stefanski and Carroll. LocallyD-optimaln-point designs are derived using the branch-and-bound algorithm of Welch. In simulations, the overall sequential designs appear to be considerably more efficient than random seeding of items.This report was prepared under the Navy Manpower, Personnel, and Training R&D Program of the Office of the Chief of Naval Research under Contract N00014-87-0696. The authors wish to acknowledge the valuable advice and consultation given by Ronald Armstrong, Charles Davis, Bradford Sympson, Zhaobo Wang, Ing-Long Wu and three anonymous reviewers.     

Effects of serial versus concurrent task sequencing an acquisition, maintenance, and generalization

Effects of serial and concurrent task presentation on skill acquisition, generalization, and maintenance were compared. Two severely retarded females participated. During serial training, items of one response class, tracing, were trained to mastery before those of a second task, vocal imitation. In the concurrent method, training on two different tasks, tracing and vocal imitation, alternated within sessions for fixed periods of time. There were no major differences between the serial and concurrent methods of instruction in the number of steps attained per behavior or in the number of trials required to reach criterion levels of performance. It was found however, that concurrent training resulted in more generalization. Retention results were not consistently related to training method.     

PROGRAMMING GENERALIZATION OF IN-CLASS TRANSITION SKILLS: TEACHING PRESCHOOLERS WITH DEVELOPMENTAL DELAYS TO SELF-ASSESS AND RECRUIT CONTINGENT TEACHER PRAISE

We investigated a self-management intervention package that taught preschoolers with developmental delays to self-assess performance of targeted skills and to recruit teacher praise. Self-assessment alone resulted in increases in active engagement across all participants during the training sessions, but generalization to classrooms was sporadic and short-lived. When recruitment of contingent praise was added to the training package, treatment effects generalized to the participants' classrooms and teachers' rates of contingent praise increased. The implications of combining self-assessment and recruitment of contingent teacher praise are discussed.     

THE NATURE OF PHYSICAL REALITY

Abstract. This account of the dynamical theory of chaos leads to a metaphysical picture of a world with an open future, in which the laws of physics are emergent-downward approximations to a more subtle and supple reality and in which there is downward causation through information input as well as upward causation through energy input. Such a metaphysical picture can accommodate both human and divine agency.     

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.