This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo…

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…

A Monte Carlo simulation was conducted to investigate the robustness of 4 latent variable interaction modeling approaches (Constrained Product Indicator [CPI], Generalized Appended Product Indicator [GAPI], Unconstrained Product Indicator [UPI], and Latent Moderated Structural Equations [LMS]) under high degrees of nonnormality of the observed…

Horn's parallel analysis (PA) is the method of consensus in the literature on empirical methods for deciding how many components/factors to retain. Different authors have proposed various implementations of PA. Horn's seminal 1965 article, a 1996 article by Thompson and Daniel, and a 2004 article by Hayton, Allen, and Scarpello all make assertions…

Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) for general covariance structure models and applied to structural equation modeling by Bollen and Stine…

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…

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Tested empirically the applicability of a method developed by S. Mattson for generating data on latent variables with controlled skewness and kurtosis of the observed variables. Monte Carlo simulation results suggest that Mattson's method appears to be a good approach to generate data with defined levels of skewness and kurtosis. (SLD)

Simulated data for factor analytic models is used in the evaluation of three methods for controlling Type I errors: (1) the standard approach that involves testing each parameter at the 0.05 level; (2) the Bonferroni approach; and (3) a simultaneous test procedure (STP). Advantages offered by the Bonferroni approach are discussed. (SLD)

Discusses the design and analysis of Monte Carlo experiments, with special reference to structural equation modeling. Outlines three fundamental challenges of Monte Carlo approaches and suggests some alternative procedures that challenge conventional wisdom. Asserts that comprehensive Monte Carlo studies can be done with a personal computer if the…

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…

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…

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)

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…