Bayesian methods for estimating dose response curves in quantal bioassay are studied. A linearized multi-stage model is assumed for the shape of the curves. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the "relative additional risk" and the "risk specific…

The asymptotic posterior normality of latent variable distributions is established under very general and appropriate hypotheses, providing a probabilistic basis for assessing ability estimation/prediction accuracy in the long test case, as well as a first step in making the Dutch Identity conjecture rigorous. (SLD)

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…

A numerical procedure is outlined for obtaining an interval estimate of a parameter in an empirical Bayes estimation problem. The case where each observed value x has a binomial distribution, conditional on a parameter zeta, is the only case considered. For each x, the parameter estimated is the expected value of zeta given x. The main purpose is…

A multiparameter, programmable model was developed to examine the interactive influence of certain parameters on the probability of deciding that an examinee had attained a specified degree of mastery. It was applied within the simulated context of performance testing of military trainees. These parameters included: (1) the number of assumed…

Standard procedures for estimating item parameters in Item Response Theory models make no use of auxiliary information about test items, such as their format or content, or the skills they require for solution. This paper describes a framework for exploiting this information, thereby enhancing the precision and stability of item parameter…

A Markov model for predicting performance on criterion-referenced tests is presented,. The model is expressed mathematically as a function of transition matrix, a current state vector, and a future state vector. The matrix is defined in terms of conditional probabilities, i.e., the probability of making a transition to a specific future…

The use of Bayesian decision theory to solve problems in test-based decision making is discussed. Four basic decision problems are distinguished: (1) selection; (2) mastery; (3) placement; and (4) classification, the situation where each treatment has its own criterion. Each type of decision can be identified as a specific configuration of one or…

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…

Methods for predicting specific college course grades, based on small numbers of observations, were investigated. These methods use collateral information across potentially diverse institutions to obtain refined within-group parameter estimates. One method, referred to as pooled least squares with adjusted intercepts, assumes that slopes and…

A predictive adaptive testing (PAT) strategy was developed based on statistical predictive analysis, and its feasibility was studied by comparing PAT performance to those of the Flexilevel, Bayesian modal, and expected a posteriori (EAP) strategies in a simulated environment. The proposed adaptive test is based on the idea of using item difficulty…

Two methods of using collateral information from similar institutions to predict college freshman grade average were investigated. One central prediction model, referred to as pooled least squares with adjusted intercepts, assumes that slopes and residual variances are homogeneous across selected colleges. The second model, referred to as Bayesian…

The validity of American College Testing Program (ACT) test scores and self-reported high school grades for predicting grades in specific college freshman courses was studied. Specific course grades are typically used to place students in remedial, standard, or advanced classes. These placement decisions, in turn, have immediate implications for…