Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output. In this paper, we review the principle of global and local sensitivity analyses of a complex black-box system. A simulated case of application is given at the end of this paper to compare both approaches.…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

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.)

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

The problem of chance model modifications under varying levels of sample size, model size, and severity of misspecification in confirmatory factor analysis models was examined through Monte Carlo simulations. Findings suggest that practitioners should exercise caution when interpreting modified models unless sample size is quite large. (SLD)

Two forms, pure-rank and mixed-rank, of a nonparametric, general, linear model-based statistic that can be used to test several hypotheses are presented. A Monte Carlo study was used to investigate the distributional properties of these forms, and their use is discussed. (SLD)

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

A Monte Carlo simulation study compared the power and Type I errors of the Wilks lambda statistic and the statistic of M. L. Puri and P. K. Sen (1971) on transformed data in a one-way multivariate analysis of variance. Preferred test procedures, based on robustness and power, are discussed. (SLD)

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. Some Monte Carlo simulations illustrate the efficacy of the procedure, which performs well with or without outliers. (SLD)

While it is imperative that attempts be made to assess the predictive accuracy of any prediction model, traditional measures of predictive accuracy have been criticized as suffering from "the base rate problem." The base rate refers to the relative frequency of occurrence of the event being studied in the population of interest, and the…

Proposes a modified version of commonly employed item response models in a fully Bayesian framework and obtains inferences under the model using Markov chain Monte Carlo techniques. Demonstrates use of the model in a series of simulations and with operational data from the North Carolina Test of Computer Skills and the Test of Spoken English…

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…

This Monte Carlo simulation studied the relative power of 8 tests for sphericity in randomized block designs where sample size was small (10, 15, 20, and 30) and population covariance matrices of dimension-to-sample size ratio approached 1.0. The locally best invariant test demonstrated substantial power to detect departures from sphericity. (SLD)