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Chun, So Yeon; Shapiro, Alexander – Multivariate Behavioral Research, 2009
The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…
Descriptors: Statistical Analysis, Structural Equation Models, Validity, Monte Carlo Methods
Wanstrom, Linda – Multivariate Behavioral Research, 2009
Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…
Descriptors: Sample Size, Effect Size, Mathematical Formulas, Computation
de Winter, J. C. F.; Dodou, D.; Wieringa, P. A. – Multivariate Behavioral Research, 2009
Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes ("N"), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for "N" below 50. Simulations were carried out to estimate the minimum required "N" for different…
Descriptors: Sample Size, Factor Analysis, Enrollment, Evaluation Methods
Yuan, Ke-Hai – Multivariate Behavioral Research, 2008
In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…
Descriptors: Monte Carlo Methods, Graduate Students, Social Sciences, Data Analysis
Shieh, Gwowen – Multivariate Behavioral Research, 2009
In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference…
Descriptors: Social Science Research, Sample Size, Monte Carlo Methods, Validity
Fan, Xitao; Sivo, Stephen A. – Multivariate Behavioral Research, 2007
The search for cut-off criteria of fit indices for model fit evaluation (e.g., Hu & Bentler, 1999) assumes that these fit indices are sensitive to model misspecification, but not to different types of models. If fit indices were sensitive to different types of models that are misspecified to the same degree, it would be very difficult to establish…
Descriptors: Structural Equation Models, Criteria, Monte Carlo Methods, Factor Analysis

Marsh, Herbert W.; Hau, Kit-Tai; Balla, John R.; Grayson, David – Multivariate Behavioral Research, 1998
Whether "more is ever too much" for the number of indicators per factor in confirmatory factor analysis was studied by varying sample size and indicators per factor in 35,000 Monte Carlo solutions. Results suggest that traditional rules calling for fewer indicators for smaller sample size may be inappropriate. (SLD)
Descriptors: Factor Structure, Monte Carlo Methods, Research Methodology, Sample Size

Kolb, Rita R.; Dayton, C. Mitchell – Multivariate Behavioral Research, 1996
Monte Carlo methods were used to evaluate an EM algorithm used for the correction of missing data in latent class analysis. Findings regarding bias in parameter estimates suggest practical limits for the utility of the EM algorithm in terms of sample size and nonresponse rate. (SLD)
Descriptors: Estimation (Mathematics), Monte Carlo Methods, Responses, Sample Size
Nevitt, Jonathan; Hancock, Gregory R. – Multivariate Behavioral Research, 2004
Through Monte Carlo simulation, small sample methods for evaluating overall data-model fit in structural equation modeling were explored. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; Satorra & Bentler, 1988, 1994), residual-based (Browne, 1984), and asymptotically…
Descriptors: Statistical Data, Sample Size, Monte Carlo Methods, Structural Equation Models

Curran, Patrick J.; Bollen, Kenneth A.; Paxton, Pamela; Kirby, James; Chen, Feinian – Multivariate Behavioral Research, 2002
Examined several hypotheses about the suitability of the noncentral chi square in applied research using Monte Carlo simulation experiments with seven sample sizes and three distinct model types, each with five specifications. Results show that, in general, for models with small to moderate misspecification, the noncentral chi-square is well…
Descriptors: Chi Square, Models, Monte Carlo Methods, Sample Size

Mendoza, Jorge L.; And Others – Multivariate Behavioral Research, 1991
Using a Monte Carlo simulation, a bootstrap procedure was evaluated for setting a confidence interval on the unrestricted population correlation (rho) assuming various degrees of incomplete truncation on the predictor. Sample size was the most important factor in determining accuracy and stability. Sample size should be at least 50. (SLD)
Descriptors: Computer Simulation, Correlation, Estimation (Mathematics), Mathematical Models

Bentler, Peter M.; Yuan, Ke-Hai – Multivariate Behavioral Research, 1999
Studied the small sample behavior of several test statistics based on the maximum-likelihood estimator but designed to perform better with nonnormal data. Monte Carlo results indicate the satisfactory performance of the "F" statistic recently proposed by K. Yuan and P. Bentler (1997). (SLD)
Descriptors: Estimation (Mathematics), Maximum Likelihood Statistics, Monte Carlo Methods, Sample Size

Spiegel, Douglas K. – Multivariate Behavioral Research, 1986
Tau, Lambda, and Kappa are measures developed for the analysis of discrete multivariate data of the type represented by stimulus response confusion matrices. The accuracy with which they may be estimated from small sample confusion matrices is investigated by Monte Carlo methods. (Author/LMO)
Descriptors: Mathematical Models, Matrices, Monte Carlo Methods, Multivariate Analysis
Shieh, Gwowen – Multivariate Behavioral Research, 2003
Repeated measures and longitudinal studies arise often in social and behavioral science research. During the planning stage of such studies, the calculations of sample size are of particular interest to the investigators and should be an integral part of the research projects. In this article, we consider the power and sample size calculations for…
Descriptors: Comparative Analysis, Behavioral Science Research, Monte Carlo Methods, Longitudinal Studies

Bandalos, Deborah L. – Multivariate Behavioral Research, 1993
A Monte Carlo study investigated the use of four cross-validation indices with confirmatory factor analysis models. Influences of sample size, loading size, and degree of model misspecification were studied. Larger sample sizes and better specified models result in better cross-validation results. (SLD)
Descriptors: Equations (Mathematics), Estimation (Mathematics), Influences, Mathematical Models