Four researchers at the Educational Testing Service describe what they consider some of the most vexing research problems they face. While these problems are not completely statistical, they all have major statistical components. Following the introduction (section 1), in section 2, "Problems with the Simultaneous Estimation of Many True…

Monte Carlo simulation was used to investigate score bias and information characteristics of Owen's Bayesian adaptive testing strategy, and to examine possible causes of score bias. Factors investigated in three related studies included effects of item discrimination, effects of fixed vs. variable test length, and effects of an accurate prior…

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)

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…

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,…

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 scaling procedure is proposed, based on item response theory (IRT), to fit non-hierarchical test structure as well. The binary scores of a test of English were used for calculating the probabilities of answering each item correctly. The probability matrix was factor analyzed, and the difficulty intervals or estimates corresponding to the factors…

ASCAL is a microcomputer-based program for calibrating items according to the three-parameter logistic model of item response theory. It uses a modified multivariate Newton-Raphson procedure for estimating item parameters. This study evaluated this procedure using Monte Carlo Simulation Techniques. The current version of ASCAL was then compared to…

Analyses for results of a series of studies examining intercorrelations among a set of as many as p+1 variables are presented. Several estimators of a pooled or average correlation vector and its variances are derived for cases in which some studies do not report complete correlation matrices. A test of the homogeneity (consistency) of the…

The issue of test-item selection in support of decision making in adaptive testing is considered. The number of items needed to make a decision is compared for two approaches: selecting items from an item pool that are most informative at the decision point or selecting items that are most informative at the examinee's ability level. The first…

Researchers have been limited in their ability to examine multiple constructs simultaneously due to the constraints imposed by traditional statistical methods. The most notable limitations include the need for a relatively large sample size while restricting the variables to a relatively small number. The application of a newly discovered…

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

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…