A detailed investigation of the statistical procedure of W. Stout (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary response data from a psychological test is presented. One finding is that DIMTEST may fail to perform as desired in the presence of guessing when…

Activities and teaching methods for developing an understanding of fractions are presented. The activities, which use mathematical models (visual representations of fractions), are divided into three sections: (1) equivalent fraction circles; (2) fraction bars; and (3) multiplication of fractional numbers using squares. Each section includes the…

LISREL-type structural equation modeling is a powerful statistical technique that seems appropriate for social science variables which are complex and difficult to measure. The literature on the specification, estimation, and testing of such models is voluminous. The greatest proportion of this literature, however, focuses on the technical aspects…

Using data from High School and Beyond, this study empirically investigated the extent of within-variable, between-occasion error covariances among variables included in educational achievement models. Little evidence was found to support the statement that reliability estimates for social background variables are inflated because of correlated…

A generalized Rasch model is presented for measuring attitudes; it is based on the concepts of Thurstone's method of successive intervals. Benefits of the model are illustrated with a study of students' (N=4,035 fifth through ninth graders) interest in physics. (SLD)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Discusses the equation and proportion methods for teaching how to solve percent problems. Supplements the teaching of each method by introducing a representational model that enhances understanding when solving percent problems. (MDH)

A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)

The common item equating method (weighted and unweighted) and the one-step missing data calibration method used with Rasch measurement models were compared using data from six equivalent forms of a perceptual ability test administered as part of the Dental Admission Test. Results suggest little difference among the equating methods. (SLD)

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

Variance formulas of H. E. Daniels and M. G. Kendall (1947) are generalized to allow for the presence of ties and variance of the sample tau correlation. Applications of these generalized formulas are discussed and illustrated using data from a 1965 study of contraceptive use in 15 developing countries. (SLD)

A Monte Carlo study explores the robustness assumption in structural equation modeling of using a full information normal theory generalized least-squares estimation procedure on Type I censored data. The efficacy of the following proposed alternate estimation procedures is assessed: asymptotically distribution free estimator and a latent…

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. For social and behavioral science applications, the developed algorithm does not rely on the assumption of multinomial errors and allows for scaling of input and output variables. (SLD)

The regression-discontinuity design involving a treatment interaction effect (TIE), pretest-posttest functional form specification, and choice of point-of-estimation of the TIE are examined. Formulas for controlling the magnitude of TIE in simulations can be used for simulating the randomized experimental case where estimation is not at the…

Four experiments with 128 college undergraduates and 82 Air Force recruits examined the coordination of a verbal component task with a visual spatial and an auditory component task. Results show that ability to coordinate perceptual and visual information differs from ability to deal with either type of information alone. (SLD)