Researchers are increasingly using observational or nonrandomized data to estimate causal treatment effects. Essential to the production of high-quality evidence is the ability to reduce or minimize the confounding that frequently occurs in observational studies. When using the potential outcome framework to define causal treatment effects, one…

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

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…

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…

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…

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)

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)

Presents an approach to multidimensional unfolding that reduces the occurrence of degenerate solutions and conducts a Monte Carlo study to demonstrate the superiority of the new method to the ALSCAL and KYST nonmetric procedures for student preference data. (SLD)

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)

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…

Procedures for implementing parallel analysis (PA) criteria in practice were compared, examining regression equation methods that can be used to estimate random data eigenvalues from known values of the sample size and number of variables. More internally accurate methods for determining PA criteria are presented. (SLD)

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

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…