Problems in selection of optimal designs in item-response theory (IRT) models are resolved through a sequential design procedure that is a modification of the D-optimality procedure proposed by Wynn (1970). This algorithm leads to consistent estimates, and the errors in selecting the abilities generally do not greatly affect optimality. (SLD)

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

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)