A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of…

Viewing the reliability for criterion-referenced tests as that of mastery classification decisions, three models for determining reliability were examined using two test administrations so that two estimates could be compared to a standard. A major purpose of the research was to determine how several reliability coefficients (coefficient kappa, an…

The 1990 National Assessment of Educational Progress (NAEP) will mark the first time that state-level comparisons will be possible with NAEP data. The 1990 data will contain, as a trial component, state-level assessments of eighth graders in mathematics. Mathematics and reading comparisons for fourth graders will be added in 1992. Statistical…

The use of a three-parameter logistic model for applying latent trait theory has become more popular because of the availability of computer programs. The program Logist 5 can be used not only for the item parameter estimation in the three-parameter logistic model, but also in the two parameter logistic model by setting the third parameter equal…

A psychometric model called Saltus, which represents the qualitative aspects of hierarchical development in a form applicable to additive measurement, was applied. Both Piaget's theory of cognitive development and Gagne's theory of learning hierarchies were used to establish the common features of hierarchical development: (1) gappiness--the…

In studies involving matrix sampling on items, it is often the case that there are too few responses per individual to use latent trait item response models. A model is formulated wherein individual level variability appears as independent error within the cells of a cross classification of demographic variables. (JKS)

Recent work in factor analysis of categorical variables is reviewed, emphasizing a generalized least squares solution and a maximum likelihood approach. A common factor model for dichotomous items is introduced, and the estimation of factor loadings from matrices of tetracorrelations is discussed. (LMO)

A stochastic multidimensional unfolding (MDU) procedure is presented to represent individual differences in phased or sequential decision processes spatially. A Monte Carlo analysis demonstrates estimation proficiency and the appropriateness of the proposed model selection heuristic, and an application to capture awareness, consideration, and…

Using longitudinal data on career paths of 3,941 special educators, maximum likelihood estimators are derived for the parameters of a discrete-time hazard model, and it is shown that the model can be fit using standard logistic regression software. Illustrative computer codes from the Statistical Analysis System (SAS) are offered. (SLD)

Bias, standard error, and reliability of five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. Results indicate that estimates based on Bayesian modal, expected a posteriori, and weighted likelihood estimators were reasonably unbiased with relatively small standard…

This edition is the 25th report in a series that began in 1964. It revises the previous edition and includes statistics on elementary and secondary schools and institutions of higher education at the national level. Included are projections for enrollment, graduates, classroom teachers, and expenditures to the year 2006. Projections are also…

Several regression methods were examined within the framework of weighted structural regression (WSR), comparing their regression weight stability and score estimation accuracy in the presence of outlier contamination. The methods compared are: (1) ordinary least squares; (2) WSR ridge regression; (3) minimum risk regression; (4) minimum risk 2;…

The reliability of four branching algorithms commonly used in computer adaptive testing (CAT) was examined. These algorithms were: (1) maximum likelihood (MLE); (2) Bayesian; (3) modal Bayesian; and (4) crossover. Sixty-eight undergraduate college students were randomly assigned to one of the four conditions using the HyperCard-based CAT program,…

This paper is the final report of a multi-year project sponsored by the Office of Naval Research (ONR) in 1987 through 1990. The main objectives of the research summarized were to: investigate the non-parametric approach to the estimation of the operating characteristics of discrete item responses; revise and strengthen the package computer…

The effectiveness of alternative procedures to correct for rater leniency/stringency effects was studied when true scores were known. Ordinary least squares, weighted least squares, and imputation of the missing data consistently outperformed averaging the observed ratings; and the imputation technique was superior to the least squares methods.…