Topics concerning latent trait theory are addressed: (1) dimensionality of latent space, local independence, and item characteristic curves; (2) models--equations, parameter estimation, testing assumptions, and goodness of fit, (3) applications test developments, item bias, tailored testing and equating; and (4) advantages over classical…

The accuracy of estimation of the subjects' latent ability maintained by tailoring for each testee the order of item presentation and the border of item dichotomization was compared to the information provided by the original graded test items. (RC)

A nonparametric multicategorical model for multiple-choice data is proposed as an extension of the binary spline model of J. O. Ramsay and M. Abrahamowicz (1989). Results of two Monte Carlo studies illustrate the model, which approximates probability functions by rational splines. (SLD)

The conventional method of measuring ability--based on items with assumed true parameter values obtained from a pretest--is compared to a Bayesian method that deals with the uncertainties of such items. Data from a 1987 American College Testing Program mathematics test indicate that maximum likelihood/Bayesian techniques underestimate uncertainty.…

When the three-parameter logistic model and item response theory are used to analyze Graduate Management Admission Test (GMAT) data, there are problems with the assumption of unidimensionality. Linear factor analytic models, exploratory factor analysis programs, and the comparison of item parameter estimates for heterogeneous and homogeneous…

A study was conducted to compare tailored testing procedures based on a Bayesian ability estimation technique and on a maximum likelihood ability estimation technique. The Bayesian tailored testing procedure selected items so as to minimize the posterior variance of the ability estimate distribution, while the maximum likelihood tailored testing…

To correct for the effects of measurement error on structural parameter estimates, many researchers are now estimating models of educational achievement with LISREL. In order to estimate such models it is desirable to obtain multiple manifest measures of the latent constructs. Many researchers restrict their models to two manifest measures per…

A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. Each item may have a different response function where each item response may be explained by one or more latent traits. Item response functions may follow a partial credit model (D. Andrich, 1978; and G. N.…

Several models for optimizing incomplete sample designs with respect to information on the item parameters are presented. The following cases are considered: (1) known ability parameters; (2) unknown ability parameters; (3) item sets with multiple ability scales; and (4) response models with multiple item parameters. The models are able to cope…

Dichotomous search strategies (DSSs) for computerized adaptive testing are similar to golden section search strategies (GSSSs). Each middle point of successive search regions is a testing point. After each item is administered, the subject's obtained score is compared with the expected score at successive testing points. If the subject's obtained…

This paper reports on a project which has developed the general latent class model as a framework for representation of item responses. This framework can be used to represent data in applications such as mastery tests and other kinds of achievement tests, where there is reason to believe that current foundations are deficient. Methods of…

Hierarchical linear modeling allowed the indentification of specific school characteristics and policies which help explain the relationship between social class and minority status with mathematics achievement, the relationship between social class and minority status with mathematics course enrollment, and school means for achievement and for…

A three-level multivariate statistical modeling strategy is presented that resolves the question of whether the unit of analysis should be the teacher or the student. A reanalysis of U.S. high school data (51 Catholic and 59 public schools from the High School and Beyond survey) illustrates the model. (SLD)

This study investigates the extent to which the higher order factors of symbolic and semantic content are differentiated. The main concern is an expository description of the use of confirmatory factor analysis in establishing factorial validity. Reanalyzed data originally collected in 1968 involved a sample of 197 tenth, eleventh and twelfth…

As part of the military recruiting effort, the Department of Defense sponsors surveys of the national youth population to help design recruiting and advertising strategies. This report develops and applies a method of using the information contained in national youth surveys to estimate the probability that respondents taking the Armed Forces…