Examines the ways in which level-1 outliers can impact the estimation of fixed effects and random effects in hierarchical models (HMs). Also outlines and illustrates the use of Markov Chain Monte Carlo algorithms for conducting sensitivity analyses under "t" level-1 assumptions, including algorithms for settings in which the degrees of…

Illustrates that sampling variance can be very large when a three-wave quasi simplex model is used to obtain reliability estimates. Also shows that, for the reliability parameter to be identified, the model assumes a Markov process. These problems are evaluated with both real and Monte Carlo data. (SLD)

A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel…

Introduces a new technique for estimating the parameters of models with continuous latent data. To streamline presentation of this Markov Chain Monte Carlo (MCMC) method, the Rasch model is used. Also introduces a new sampling-based Bayesian technique, the DA-T-Gibbs sampler. (SLD)

Discusses three types of least squares estimation (generalized, unweighted, and weighted). Results from a Monte Carlo simulation show that, in comparison with other least squares methods, the weighted least squared method generally reduced bias without increasing asymptotic standard errors. (SLD)

For complex educational assessments, there is an increasing use of "item families," which are groups of related items. However, calibration or scoring for such an assessment requires fitting models that take into account the dependence structure inherent among the items that belong to the same item family. C. Glas and W. van der Linden…

Presents sports-oriented examples (cricket and football) in which Monte Carlo methods are used on microcomputers to teach probability concepts. Both examples include computer programs (with listings) which utilize the microcomputer's random number generator. Instructional strategies, with further challenges to help students understand the role of…