There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

A short review of the different estimation procedures that have been used in association with the Rasch model is provided. These procedures include joint, conditional, and marginal maximum likelihood methods; Bayesian methods; minimum chi-square methods; and paired comparison estimation. A comparison of the marginal maximum likelihood estimation…

The proper use of Pearson's chi-square for the analysis of contingency tables is reviewed. A 1949 article by Lewis and Burke, in which they cite nine primary sources of error in the use of chi-square, serves as the basis of the review. Those nine sources of error are re-examined in light of current research. In addition, techniques and research on…

Some item response theory (IRT) techniques work in applications even though the usual structural IRT assumptions, and local independence (LI) in particular, do not hold. When the departure from LI is too great, traditional procedures will break down. Although violations of strictly unidimensional, monotone, locally independent latent structure can…

This report summarizes the research findings of a four year contract investigating the applicability of item response theory and tailored testing to criterion-referenced measurement. Six major areas were studied on the project: (1) techniques for forming unidimensional item sets; (2) techniques for calibrating items; (3) item parameter linking…

Despite advances in common factor analysis, a review of 89 studies published in four selected journals between 1963 and 1976 indicated that behavioral scientists preferred principal components analysis, followed by varimax or orthogonal rotation. Resultant row sums of squares of factor matrices from principal component analyses of real data sets…

This paper reviews the literature about item response models for the subject level and aggregated level (group level). Group-level item response models (IRMs) are used in the United States in large-scale assessment programs such as the National Assessment of Educational Progress and the California Assessment Program. In the Netherlands, these…

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

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…

Research on the major computerized adaptive testing (CAT) strategies is reviewed, and some findings are reported that examine effects of examinee demographic and psychological characteristics on CAT strategies. In fixed branching strategies, all examinees respond to a common routing test, the score of which is used to assign examinees to a…