In this paper, the efficiency of conditional maximum likelihood (CML) and marginal maximum likelihood (MML) estimation of the item parameters of the Rasch model in incomplete designs is investigated. The use of the concept of F-information (Eggen, 2000) is generalized to incomplete testing designs. The scaled determinant of the F-information…

Trait psychology implicitly assumes consistency of the personal traits. Mischel, however, argued against the idea of a general consistency of human beings. The present article aims to design a statistical procedure based on an adaptation of the pi* statistic to measure the degree of intraindividual consistency independently of the measure used.…

Biological phenomena can be investigated at multiple levels, from the molecular to the cellular to the organismic to the ecological. In typical biology instruction, these levels have been segregated. Yet, it is by examining the connections between such levels that many phenomena in biology, and complex systems in general, are best explained. We…

The extent to which a scale score generalizes to a latent variable common to all of the scale's indicators is indexed by the scale's general factor saturation. Seven techniques for estimating this parameter--omega[hierarchical] (omega[subscript h])--are compared in a series of simulated data sets. Primary comparisons were based on 160 artificial…

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

Recent studies have reported that preverbal infants are able to discriminate between numerosities of sets presented within a particular modality. There is still debate, however, over whether they are able to perform intermodal numerosity matching, i.e. to relate numerosities of sets presented with different sensory modalities. The present study…

Over the past 3 decades we have witnessed an increase in the complexity of theoretical models that attempt to explain development in a number of behavioral domains. The conceptual movement to examine behavior from both developmental and contextual perspectives parallels recent methodological advances in the analysis of change. These new analysis…

A latent variable modeling approach to reliability and measurement invariance evaluation for multiple-component measuring instruments is outlined. An initial discussion deals with the limitations of coefficient alpha, a frequently used index of composite reliability. A widely and readily applicable structural modeling framework is next described…

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…

We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the…

This article describes a simple way to demonstrate powder diffraction in a classroom setting using a dry film of spherical colloids on a glass substrate. Use of transparent, elastomeric poly(dimethylsiloxane) as a supporting substrate for the spheres rather than glass enables demonstration of the reciprocal lattice effect. (Contains 4 figures and…

Purpose: Family caregivers comprise the backbone of long-term-care provision in the United States, yet little is known about how the composition and experience of family caregiving has changed over time. Design and Methods: Data are drawn from the 1989 and 1999 National Long-Term Care Survey and Informal Caregiver Survey to develop nationally…

This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom…