Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of dichotomous items. The algorithms presented, and three competing deterministic algorithms are compared using computer-generated data. (Author/JKS)

The model presented involves the concept of "mathematical quotient." It is intended that the model be used by the classroom teacher in developing mathematical instructional sequences. (MK)

The relationship between hierarchical linear modeling (HLM) notation and mixed model notation is illustrated by explicitly mapping the parameters across notations for a concrete example involving the hierarchical modeling of change. (Author/SLD)

Describes the individual chapters of this collection and notes that, although the book lacks consistency in some respects, it contains state-of-the-art reflections on the modeling of change and should stimulate discussion for experts and practitioners. (SLD)

Studied whether empirical multitrait multioccasion (MTMO) data conform more closely to multiplicative models than to additive models, using four additive models and two versions of the multiplicative Direct Product model. Results based on matrices from previous studies show that both additive and multiplicative models usually fit the same MTMO…

Compared two methods for developing a common metric for the graded response model under item response theory: (1) linking separate calibration runs using equating coefficients from the characteristic curve method; and (2) concurrent calibration using the combined data of the base and target groups. Concurrent calibration yielded consistently,…

Three potential models for the 2 X 2 contingency table are discussed: (1) the hypergeometric Independence Trial; (2) the double-binomial Comparative Trial; and (3) the multinomial Double Dichotomy Trial. Subsequently, the critical regions of seven statistical tests are evaluated within each of these models. (TJH)

Presents a necessary and sufficient condition for the equivalence of structural-equation models that is applicable to models with parameter restrictions and models that may or may not fulfill assumptions of the rules. Illustrates the application of the approach for studying model equivalence. (SLD)

Latent variable models for an infinite sequence (or universe) of manifest variables that may be discrete, continuous, or a combination of both, are considered. A main theorem is presented that characterizes when it is possible to construct latent variable models that satisfy unidimensionality, monotonicity, conditional independence, and tail…

Defines a random effects diagonal metric multidimensional scaling model, gives its computational algorithms, describes researchers' experiences with these algorithms, and provides an illustration of the use of the model and algorithms. (Author/SLD)

Proposed minimax designs for item response theory (IRT) models to overcome the problem of local optimality. Compared minimax designs to sequentially constructed designs for the two parameter logistic model. Results show that minimax designs can be nearly as efficient as sequentially constructed designs. (Author/SLD)

Presents examples of egregious errors of interpretation in time-series intervention models and makes recommendations regarding the correct specification of the design matrix. Discusses the profound effects of variants of the slope change variable in the design matrix. (SLD)

Quantitative psychology is concerned with the development and application of mathematical models in the behavioral sciences. Over time, models have become more complex, a consequence of the increasing complexity of research designs and experimental data, which is also a consequence of the utility of mathematical models in the science. As models…

A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…

Students majoring in Management Information Systems (MIS) are required to take a course in Decision Support Systems (DSS) as part of their information systems core at this university. In a typical course on DSS, students are taught about use of mathematical models for solving large complex problems. They learn about the power, efficiency,…