Diffusion-based item response theory models for responses and response times in tests have attracted increased attention recently in psychometrics. Analyzing response time data, however, is delicate as response times are often contaminated by unusual observations. This can have serious effects on the validity of statistical inference. In this…

Multilevel models (MLMs) have proven themselves to be very useful in social science research, as data from a variety of sources is sampled such that individuals at level-1 are nested within clusters such as schools, hospitals, counseling centers, and business entities at level-2. MLMs using restricted maximum likelihood estimation (REML) provide…

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…

The robustness and power of 9 strategies for testing the differences in groups' regression slopes were assessed under nonnormality and residual variance heterogeneity. For the conditions considered, the most robust strategies were the trimmed and Winsorized slope estimates used with the James second-order test, the Theil-Sen slope estimates used…

Recently, C. E. McCulloch (1987) suggested a modification of the Morgan-Pitman test for comparing the variances of two dependent groups. This paper demonstrates that there are situations where the procedure is not robust. A subsample approach, similar to the Box-Scheffe test, and the Sandvik-Olsson procedure are also assessed. (TJH)

A maximum likelihood approach to correlational outlier identification is introduced and compared to the Mahalanobis D squared and Comrey D statistics through Monte Carlo simulation. Identification performance depends on the nature of correlational outliers and the measure used, but the maximum likelihood approach is the most robust performance…

Simulation studies (N=4,000 simulees) examined the effect of misspecification of the latent ability distribution (theta) on the accuracy and efficiency of marginal maximum likelihood (MML) item parameter estimates and on MML statistics to test sufficiency and conditional independence. Results were compared to those of the conditional maximum…

A Monte Carlo study was conducted to assess the robustness of the limited information two-stage least squares (2SLS) estimation procedure on a confirmatory factor analysis model with nonnormal distributions. Full information maximum likelihood methods were used for comparison. One hundred model replications were used to generate data. (TJH)

By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the…