This study presents the random-effects rating scale model (RE-RSM) which takes into account randomness in the thresholds over persons by treating them as random-effects and adding a random variable for each threshold in the rating scale model (RSM) (Andrich, 1978). The RE-RSM turns out to be a special case of the multidimensional random…

In the educational literature, responses to surveys commonly serve as the source of data for many empirical articles. Whenever a survey is used as a source of data, the response rate can greatly affect the potential generalizability of the findings. Using Monte Carlo methods, this study examined the effects on sample estimates of the population…

This research explored the degree to which group sizes can differ before the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are jeopardized. Monte Carlo methodology was used, allowing for the experimental investigation of potential threats to robustness under conditions common to researchers in education. The…

Current omnibus procedures for the analysis of interaction effects in repeated measures designs which contain a grouping variable are known to be nonrobust to violations of multisample sphericity, particularly when group sizes are unequal. An alternative approach is to formulate a comprehensive set of contrasts on the data which probe the specific…

This study investigated and compared the properties of five methods of item exposure control within the purview of estimating examinees' abilities in a computerized adaptive testing (CAT) context. Each of the exposure control algorithms was incorporated into the item selection procedure and the adaptive testing progressed based on the CAT design…

This study presents an overview of Monte Carlo studies in discriminant analysis. Some common questions about the use of Monte Carlo techniques are answered through a brief literature review of articles on discriminant analysis in which Monte Carlo methods are used. The articles cover many research points, such as comparing error rate estimates,…

Monte Carlo simulation is a computer modeling procedure for mimicking observations on a random variable. A random number generator is used in generating the outcome for the events that are being modeled. The simulation can be used to obtain results that otherwise require extensive testing or complicated computations. This paper describes how Monte…

Focuses on three management tools--the Delphi technique, Bayesian statistics, and Monte Carlo simulation--in order to simulate a problem-solving/decision-making situation with which an educational administrator may be faced. (Author)

A Monte Carlo study was done to determine the adequate sample size for quasi-experimental regression studies, which compare regression lines for two groups and estimate their point of intersection. Populations of 1,000 subjects in each of two groups were constructed (using random normal deviates) to yield equivalent regression lines of opposite…

Numerous designs using analysis of variance (ANOVA) to test ordinal hypotheses were assessed using a Monte Carlo simulation. Each statistic was computed on each of over 10,000 random samples drawn from a variety of population conditions. The number of groups, population variance, and patterns of population means were varied. In the non-null…

The dynamic linear model or Kalman filtering model provides a useful methodology for predicting the past, present, and future states of a dynamic system, such as an object in motion or an economic or social indicator that is changing systematically with time. Recursive likelihood methods for adaptive Kalman filtering and smoothing are developed.…

Two bootstrapping or resampling strategies were investigated to determine their applicability to estimating standard errors and ensuing confidence intervals on variance components in two-factor random analysis of variance models. In light of prior negative findings regarding the application of bootstrapping to this particular problem, a…

Occasionally, situations arise where mixtures of two binomials with one known success parameter are met. An example in educational testing is the mastery or random guessing model in which an examinee is supposed either to master the items or not to master them and to guess blindly. This paper gives moment estimators for such mixtures and presents…

Comparisons of corresponding values of phi and kappa coefficients were made for 270 instances of data generated by a Monte Carlo technique to simulate a test-retest situation. Data were generated for distributions with the same mean but three different levels of standard deviation, standard error of measurement and cutting score. Ten samples of…

This study compared three approaches to the two-factor experiment with repeated measures on one factor: (1) the conventional mixed model analysis of variance, (2) the Greenhouse-Geisser conservative analysis of variance, and (3) multivariate extensions of analysis of variance. Computer simulated data were used in a total of 96 sets of covariance…