Discusses information production processes (IPP)--i.e., continuous mathematical models of production processes such as bibliographies, economic production processes, and social usages of words in a text--from the point of view of concentration theory. Gini's index is studied in the dual framework of IPPs. (27 references) (LRW)

The phimax adjustment to phi (Pearson's product moment correlation applied to binary data) is explored. Phi/phimax is shown to be a measure of relationship apart from its affiliation with phi. The relations between phi/phimax and kappa and limitations of phi/phimax are discussed. (SLD)

Rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, is discussed. Rowwise and columnwise indices are particularly suited for evaluating different types of conjectures of a similar pattern of entries across the two matrices. (SLD)

Multiple imputations for latent variables are constructed so that analyses treating them as true variables have the correct expectations for population characteristics. Analyzing multiple imputations in accordance with their construction yields correct estimates of population characteristics, whereas analyzing them as multiple indicators generally…

A new version of the standardized estimated parameter change that is invariant to the original metrics of the measured and latent variables is suggested for use in model modification. A multivariate estimated parameter change for a set of fixed parameters to be freed simultaneously is also introduced. (SLD)

Extends joint maximum likelihood estimation for the hyperbolic cosine model to the situation in which the units of items are allowed to vary. Describes the four estimation cycles designed to address four important issues of model development and presents results from two sets of simulation studies that show reasonably accurate parameter recovery…

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variable as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The proposed estimation methods are illustrated by two simulation studies. (SLD)

Two studies address the sequence of understandings evident in preschoolers' developing theory of mind. The first, preliminary study provides a meta-analysis of research comparing different types of mental state understandings (e.g., desires vs. beliefs, ignorance vs. false belief). The second, primary study tests a theory-of-mind scale for…

The purpose of this article is to describe how, within the Dutch approach to mathematics education, called "Realistic Mathematics Education" (RME), models are used to elicit students' growth in understanding of mathematics. First some background information is given about the characteristics of RME related to the role of models in this approach.…

A mathematical model of a non-ideal solution is presented, where it is shown how and where the non-ideality manifests itself in the standard thermodynamics tableau. Examples related to the non-ideal solution thermodynamics study are also included.

Current descriptions of results from hierarchical linear models (HLM) and hierarchical generalized linear models (HGLM), usually based only on interpretations of individual model parameters, are incomplete in the presence of statistically significant and practically important "slopes as outcomes" terms in the models. For complete description of…

A multivariate reduced-rank growth curve model is proposed that extends the univariate reduced rank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way…

This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A…

We report on a small scale study with six experienced teachers of mathematics in which we have applied a general theoretical model of expert practice (developed by the second author) to explore the nature of the knowledge base that enables teachers to operate effectively in the complexity of a class of 30 pupils. This model uses the notion of…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…