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…

Field experiments with nested structures are becoming increasingly common, especially designs that assign randomly entire clusters such as schools to a treatment and a control group. In such large-scale cluster randomized studies the challenge is to obtain sufficient power of the test of the treatment effect. The objective is to maximize power…

Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors…

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's…

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…

Developed a sample-based nonanalytical degrees-of-freedom correction factor for situations sampling both subjects and conditions with measurement data departing from essentially parallel form. Assessed the application of this correction factor through a simulation study involving data sets with a range of design characteristics and manifesting…

Estimated empirical Type I error rate and power rate for three procedures for analyzing multivariate repeated measures designs: (1) the doubly multivariate model; (2) the Welch-James multivariate solution (H. Keselman, M. Carriere, a nd L. Lix, 1993); and (3) the multivariate version of the modified Brown-Forsythe procedure (M. Brown and A.…

Two studies, both using Type 12 sampling, are presented in which the effects of violating the assumption of essential parallelism in setting confidence intervals are studied. Results indicate that as long as data manifest properties of essential parallelism, the two methods studied maintain precise Type I error control. (SLD)

Reviews methods for analyzing repeated measures data in addition to the conventional and corrected degrees of freedom univariate and multivariate solutions. Reviews the literature regarding recent procedures with respect to robustness, ability to handle missing data, and availability of software to obtain numerical results. (SLD)

Effects of sample size and composition are systematically examined on the replicability of principal components, using observer ratings of personality from the California Adult Q-Set for 192 series of principal components analyses. Results indicate that dimensionality cannot be inferred from component robustness; they are empirically and logically…

Methods for testing hypotheses concerning the regression parameters in linear models for the latent person parameters in item response models are presented. Three tests are outlined: A likelihood ratio test, a Lagrange multiplier test and a Wald test. The tests are derived in a marginal maximum likelihood framework. They are explicitly formulated…

The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly…

The common marketing research practice of standardizing the columns of a persons-by-variables data matrix prior to clustering the entities corresponding to the rows was evaluated with 10 large-scale data sets. Results indicate that the column standardization practice may be problematic for some kinds of data that marketing researchers used for…

The Welch-James (WJ) and the Huynh Improved General Approximation (IGA) tests for interaction were examined with respect to Type I error in a between- by within-subjects repeated measures design when data were non-normal, non-spherical and heterogeneous, particularly when group sizes were unequal. The tests were computed with aligned ranks and…