Mathematical models and the experimental analysis of behavior

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists.     

An estimating equations approach for the LISCOMP model

Maximum likelihood estimation is computationally infeasible for latent variable models involving multivariate categorical responses, in particular for the LISCOMP model. A three-stage generalized least squares approach introduced by Muthén (1983, 1984) can experience problems of instability, bias, non-convergence, and non-positive definiteness of weight matrices in situations of low prevalence, small sample size and large numbers of observed indicator variables. We propose a quadratic estimating equations approach that only requires specification of the first two moments. By performing simultaneous estimation of parameters, this method does not encounter the problems mentioned above and experiences gains in efficiency. Methods are compared through a numerical study and an application to a study of life-events and neurotic illness.The authors would like to thank Bengt Muthén for many helpful discussions and Scott Henderson for generously providing the Canberra data set. This work was supported in part by grant number GM49909 of the National Institutes of Health.     

A compactness theorem for linear equations

It is proved that a system of linear equations over an arbitrary field has a solution if every finite subsystem has a solution provided that the set of variables can be well ordered.Presented by J. Zygmunt     

Products of modal logics and tensor products of modal algebras

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto's results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.     

Global problems,globalization, and predictability

The term globalization is questioned in its validity and applicability to structures other than verbal. Globalization is a historical term which changes its meaning with time and culture. It is not only that its content changes but the validity of a globalization concept changes with the historical perspective. Morever, solution of global problems depends heavily on the correct analysis of the problem. Without such an analysis there is no possibility to find even an approximate solution. Hence, predictability is impossible. There is no trend which is sufficiently long to make any reliable prediction for global problems other than the most simple ones.     

On the Escaig obstacle hypothesis for cross-slip in face-centered-cubic materials

There is a significant body of literature wherein a linear approximation of Escaig's model is used to justify the large experimentally measured activation-volumes for cross-slip in face-centered-cubic copper. Here, by examining the error between the linear approximation and the original theory, we show that this explanation is not satisfactory. The calculated value for activation volume in copper, using Escaig's original equations, yields ～60b ³ (b?=?Burgers vector) while the linear approximation yields 200b ³, the latter result fortuitously matching the experimental values.     

Structural equations modeling: Fit Indices,sample size,and advanced topics

This article is the second of two parts intended to serve as a primer for structural equations models for the behavioral researcher. The first article introduced the basics: the measurement model, the structural model, and the combined, full structural equations model. In this second article, advanced issues are addressed, including fit indices and sample size, moderators, longitudinal data, mediation, and so forth.     

Moral Management Methodology/Mythology: Erroneous Ethical Equations

Understanding the falsity of certain common beliefs helps students move toward better business ethics and a higher degree of moral management. This article explains one method for teaching moral management, by using ethical equation inequalities, and offers 10 implications and suggestions to managers.