A model is presented that demonstrates that a random response to external constraint can produce results similar to those predicted by more complex models. Behavior that appears rational, optimal, or adaptive may truly be a random response to external constraint. Predictions based on this model may provide appropriate null hypotheses. (SLD)

Studied whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. An example illustrates that neither the factor loading estimates nor the standard error estimates possess scale…

An item response theory model based on the Rasch model is proposed for composite tasks, those decomposed into subtasks of different kinds. The model, which is illustrated with an application to spelling tasks, constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the subtask items. (SLD)

Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom justified. Uses the data itself to motivate mathematical models in introductory mathematics courses. Illustrates various regression and optimization techniques. (Author/ASK)

Estimates a college-attendance equation for a common set of students (from the High School and Beyond Survey) using three popular econometric specifications: the multinomial logit, the ordered probit, and the bivariate probit. Estimated marginal effects do not differ significantly across the three specifications. Choice of specification may not…

Using 1990-91 data for 143 Ph.D. granting institutions, this study applies a simultaneous equation model to determine whether an institution's amount of research grants is a function of its academic ranking. Results show a simultaneous relationship among grants per full-time-equivalent enrollment, institutional ranking, and graduate students as a…

Defines a mathematical model of uniform response bias (URB) and proposes ipsative measures to minimize the effect of URB in multigroup confirmatory factor analysis. Illustrates the method using real data from the Chinese Personality Assessment Inventory for 2 groups of sample sizes 793 and 792 adults. (SLD)

Reports on a study comparing the use of Multi-base arithmetic blocks (MAB) and an alternative, LAB (linear arithmetic blocks) on the basis of epistemic fidelity and accessibility for students. Use of LAB was associated with more active engagement by students and deeper discussion. (Author/MM)

Dimension analysis is promoted as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Dimensional analysis is shown to lead to interesting systems of linear equations to solve, and can point the way to more quantitative analysis. Two student problems are discussed. (Author/MM)

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

A core assumption of the standard multiple regression model is independence of residuals, the violation of which results in biased standard errors and test statistics. The structural equation model (SEM) generalizes the regression model in several key ways, but the SEM also assumes independence of residuals. The multilevel model (MLM) was…

A simplified mathematical model for the calculation of imprecision associated with the construction of a calibration line is presented. The model also aims at a discussion on variables that really affect it and to integrate the resulting imprecision with that caused by the other steps in the analytical method in order to calculate a real…

This paper deals with an empirical study, which aims at showing the effects of the integration of modelling tasks into daily school routine in a comprehensive manner. At first the theoretical and methodological approach is explained. The main part of the paper deals with the results of the study. On the one hand the results show obstacles to the…

We discuss application of the Thomas-Reiche-Kuhn sum rule to simple quantum-mechanical models and its apparent violation by the rigid rotator.