This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)

Demonstrates Markov chain Monte Carlo (MCMC) techniques that are well-suited to complex models with Item Response Theory (IRT) assumptions. Develops an MCMC methodology that can be routinely implemented to fit normal IRT models, and compares the approach to approaches based on Gibbs sampling. Contains 64 references. (SLD)

The latent trait-state-error model (TSE) and the latent state-trait model with autoregression (LST-AR) represent creative structural equation methods for examining the longitudinal structure of psychological constructs. Application of these models has been somewhat limited by empirical or conceptual problems. In the present study, Monte Carlo…

Monte Carlo methodologies are frequently applied to study the sampling distribution of the estimated proficiency level in adaptive testing. These methods eliminate real situational constraints. However, these Monte Carlo methodologies are not currently supported by the available software programs, and when these programs are available, their…

The authors present a method that ensures control over the Type I error rate for those who visually analyze the data from response-guided multiple-baseline designs. The method can be seen as a modification of visual analysis methods to incorporate a mechanism to control Type I errors or as a modification of randomization test methods to allow…

When constructed response test items are scored by more than one rater, the repeated ratings allow for the consideration of individual rater bias and variability in estimating student proficiency. Several hierarchical models based on item response theory have been introduced to model such effects. In this article, the authors demonstrate how these…

A computer program which allows the solution of a Monte Carlo simulation (probabilistic sensitivity analysis) has been developed for the Vic-20 microcomputer. Theory of Monte Carlo simulation, program capabilities and operation, and sample calculations are discussed. Student comments on the program are included. (JN)

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)

Proposes a procedure for generating multivariate nonnormal distributions. The procedure, an extension of the Fleishman power method (A. Fleishman, 1978), generates the average value of intercorrelations much closer to population parameters than competing procedures for skewed and heavy tailed distributions and small sample sizes. Reports Monte…

The authors used a Monte Carlo simulation to examine how the violation of the exchangeability assumption affects empirical Type I error rates of the LMH randomization test (J. R. Levin, L. A. Marascuilo, & L. J. Hubert, 1978). Simulation results showed that the LMH test is not always an appropriate technique for analyzing systematic designs when…

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters.…

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

An active area in psychometric research is coordinated task design and statistical analysis built around cognitive models. Compared with classical test theory and item response theory, there is often less information from observed data about the measurement-model parameters. On the other hand, there is more information from the grounding…

This paper aims to describe a Bayesian approach to modeling and estimating cognitive models both in terms of statistical machinery and actual instrument development. Such a method taps the knowledge of experts to provide initial estimates for the probabilistic relationships among the variables in a multivariate latent variable model and refines…