Assessing achievement is a complex task due to its dependence on multiple factors and the hierarchical structure of educational data, yet surveys like TIMSS offer valuable insights into its determining factors like students' mathematics anxiety. However, disregarding the nested structure of data and ignoring the assumptions of models causes poor…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. (Author/LMO)

The partial credit model with a varying slope parameter is developed and called the generalized partial credit model (GPCM). Analysis results for simulated data by this and other polytomous item-response models demonstrate that the rating formulation of the GPCM is adaptable to the analysis of polytomous item responses. (SLD)

The derivation of several item selection algorithms for use in fitting test items to target information functions is described. These algorithms circumvent iterative solutions by using the criteria of moving averages of the distance to a target information function and simultaneously considering an entire range of ability points used to condition…

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 two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

This paper discusses the use of latent class structure as a modelling framework for tests in which much of the data conforms to a relatively small number of systematic patterns. Application of this framework to the analysis of tests has been limited because available parameter estimation algorithms can only handle a relatively small number of…