Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

A lognormal model for the response times of a person on a set of test items is investigated. The model has a parameter structure analogous to the two-parameter logistic response models in item response theory, with a parameter for the speed of each person as well as parameters for the time intensity and discriminating power of each item. It is…

A study was conducted to evaluate the feasibility of using item response theory (IRT) equating to reduce test form overlap of the Graduate Record Examinations (GRE) Subject Test in Mathematics. Monte Carlo methods were employed to compare double-part equating with 20-item common item blocks to triple-part equating with 10-item common item blocks.…

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…

Though common structural equation modeling (SEM) methods are predicated upon the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to use distribution-free estimation methods. Fortunately, promising alternatives are being integrated into…

Effects of test length, sample size, and assumed ability distribution were investigated in a multiple replication Monte Carlo study under the 1-parameter (1P) and 2-parameter (2P) logistic graded model with five score levels. Accuracy and variability of item parameter and ability estimates were examined. Monte Carlo methods were used to evaluate…

The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects…

Monte Carlo methods were employed to assess the relative power of the paired samples t test and Wilcoxon's signed-ranks test under ten population shapes. Results of the study indicated that: (1) each of the two statistics was more powerful than the other in given situations; (2) the power advantages of the t test under normal theory were small;…

This paper describes DATASIM, a comprehensive software package which generates simulated data for actual or hypothetical research designs. DATASIM is primarily intended for use in statistics and research methods courses, where it is used to generate "individualized" datasets for students to analyze, and later to correct their answers.…

False-positive and false-negative dicisions are the fundamental errors committed with a mastery test; yet the estimation of the likelihood of committing these errors has not been investigated. Accordingly, two methods of estimating the likelihood of committing these errors are described and then investigated using Monte Carlo techniques.…

The power of the classical Linear Discriminant Function (LDF) is compared, using Monte Carlo techniques with five other procedures for classifying observations from certain non-normal distributions. The alternative procedures considered are the Quadratic Discriminant Function, a Nearest Neighbor Procedure with Probability Blocks, and three density…

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four "classical" lower bounds to reliability. (Author/JAZ)

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…

It has been suggested that IQ's of gifted children resemble parents less than do people in general. This finding may have been an artifact of the particular estimator of the regression coefficient used. An unbiased estimator is introduced and shows that gifted children resemble parents more than persons in general. (Author/RD)

Within-class regression is a method, developed in this paper, of comparing a large number of nonequivalent groups. This study indicated that within-class regression was a less biased method of data analysis and will yield more accurate estimates of treatment effects than analysis of covariance. (PN)