This study compared the effectiveness of 10 methods of determining the number of factors to retain in exploratory common factor analysis. The 10 methods included the Kaiser rule and a modified Kaiser criterion, 3 variations of parallel analysis, 4 regression-based variations of the scree procedure, and the minimum average partial procedure. The…

Many multivariate statistical methods call upon the assumption of multivariate normality. However, many applied researchers fail to test this assumption. This omission could be due to ignorance of the existence of tests of multivariate normality or confusion about which test to use. Although at least 50 tests of multivariate normality exist,…

This study focused on the issue of measurement reliability and its attenuation on correlation between two composites and two seemingly different approaches for correcting the attenuation. As expected, Monte Carlo simulation results show that correlation coefficients uncorrected for measurement error are systematically biased downward. For the data…

The distinction between Type 1 and Type 12 sampling in connection with measurement data is discussed, and a method is presented for simulating data arising from Type 12 sampling. A Monte Carlo study is described that shows conditions under which precise confidence level control under Type 12 sampling is maintained. (SLD)

Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)

Conducted a Monte Carlo study to compare various approaches to detecting differential item functioning (DIF) under a conceptualization of DIF that recognizes that observed data are a mixture of data from multiple latent populations or classes. Demonstrated the usefulness of the approach. (SLD)

Studied four different approaches for handling missing data for their capacity to mitigate against the effect of omitted responses on person location estimation. Results from a Monte Carlo study show that the hot-decking procedure performed best of the methods examined. (SLD)

Investigated the effects of types and prevalence of response patterns that might be provided by nonattending respondents on Cronbach's alpha (L. Cronbach, 1970) using three simulated data sets. Effects were greater as a function of increased prevalence in the respondent group, but as few as 5% of some types of nonattending patterns had inflating…

Examined the optimal value of "k" for promax factor rotations through a Monte Carlo study involving 10,080 factor analyses. Results show that in factor-analytic studies using promax, the value of "k" may be set appropriately at 2, 3, or 4. (Author/SLD)

Illustrates the design and planning of Monte Carlo simulations, presenting nine steps in planning and performing a Monte Carlo analysis from developing a theoretically derived question of interest through summarizing the results. Uses a Monte Carlo simulation to illustrate many of the relevant points. (SLD)

Assessed two models for confirmatory factor analysis of multitrait-multimethod data through Monte Carlo simulation. The correlated traits-correlated methods (CTCM) and the correlated traits-correlated uniqueness (CTCU) models were compared. Results suggest that CTCU is a good alternative to CTCM in the typical multitrait-multimethod matrix, but…

Used Monte Carlo methods to evaluate the adequacy of cluster analysis to recover group membership based on simulated latent growth curve (LCG) models. Cluster analysis failed to recover growth subtypes adequately when the difference between growth curves was shape only. Discusses circumstances under which it was more successful. (SLD)

Presents a variable selection heuristic for nonhierarchical (K-means) cluster analysis based on the adjusted Rand index for measuring cluster recovery. Subjected the heuristic to Monte Carlo testing across more than 2,200 datasets. Results indicate that the heuristic is extremely effective at eliminating masking variables. (SLD)

An exercise is presented in which the kinetics of the irreversible "reaction" of pennies in the heads-up state to pennies in the tails-up state is simulated by a hands-on, Monte Carlo approach. In addition, the exercise incorporates a second simulation in which the irreversible "reaction" of dice with a red face uppermost to a blue face uppermost…

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all…