Various types of finite mixtures of confirmatory factor analysis models are proposed for handling data heterogeneity. Proposed classes of mixture models differ in their unique representations of data heterogeneity, and three sampling schemes for these mixtures are distinguished. Advantages of the Approximate Scoring method are outlined. (SLD)

The Schmid-Leiman (J. Schmid and J. M. Leiman, 1957) decomposition of a hierarchical factor model converts the model to a constrained case of a bifactor model with orthogonal common factors that is equivalent to the hierarchical model. This article discusses the equivalence of the hierarchical and bifactor models. (Author/SLD)

The idea of test consistency is illustrated, with reference to two sets of test scores. A mathematical model is used to explain the relative consistency and relative inconsistency of measurements, and a means of indexing reliability is derived using the model. Practical aspects of estimating reliability are considered. (TJH)

A theorem is developed to show that the Kruskal-Wallis test (W. Kruskal and W. Wallis, 1952) (KWt) can be used validly to test a hypothesis about location under much less restrictive conditions than required by the recently accepted, mathematically correct shift model. The specific null hypothesis for which the KWt can be used validly is…

Demonstrated that the extra-factor phenomenon (the two-dimensional solution produced when linear factor analysis is applied to a set of unfoldable items) arises because the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model and the unidimensional quadratic factor model is not distinguishable from the…

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family that includes many useful models. A three-step procedure is presented for analyzing data sets by generalized bilinear models. (SLD)

Used simulation to study two different approaches to latent variable interaction modeling with continuous observed variables: (1) a LISREL 8.30 program and (2) data analysis through PRELIS2 and SIMPLIS programs. Results show that parameter estimation was similar but standard errors were different. Discusses differences in ease of implementation.…

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

Describes methods for fitting a fuzzy consensus partition to a set of partitions of the same set of objects. Describes and illustrates three models defining median partitions and compares these methods to an alternative approach to obtaining a consensus fuzzy partition. Discusses interesting differences in the results. (SLD)

There is a growing consensus that developmental dyslexia is associated with a phonological-core deficit. One symptom of this phonological deficit is a subtle speech-perception deficit. The auditory basis of this deficit is still hotly debated. If people with dyslexia, however, do not have an auditory deficit and perceive the underlying acoustic…

A mathematical model of working-memory capacity limits is proposed on the key assumption of mutual interference between items in working memory. Interference is assumed to arise from overwriting of features shared by these items. The model was fit to time-accuracy data of memory-updating tasks from four experiments using nonlinear mixed effect…

A new mathematical tool, known as Engage, Explore, Explain (EEE) model, was developed that was simple for teachers to use, could guide them as they planned exploratory experiences, and was useful to teach mathematics for understanding. The EEE model provides a lesson structure for teachers to use with almost any mathematics topic and can easily be…

Recent events have led to an increased interest in emerging infectious diseases. This article applies various deterministic models to the SARS epidemic of 2003 and a measles outbreak in the Netherlands in 1999-2000. We take a historical approach beginning with the well-known logistic curve and a lesser-known extension popularized by Pearl and Reed…

Purpose: The purpose of this paper is to present a mathematical model that can be used as an educational tool to reflect the philosophical aspects of sustainability. Design/methodology/approach: This is a descriptive paper. Findings: Everyone carries a sustainability deficit. Therefore, opportunities to reduce this deficit abound. Education is an…

Multilevel models have come to play an increasingly important role in many areas of social science research. However, in contrast to other modeling strategies, there is currently no widely used approach for graphically diagramming multilevel models. Ideally, such diagrams would serve two functions: to provide a formal structure for deriving the…