This Monte Carlo study assessed Type I error in differential item functioning analyses using Lord's chi-square (LC), Likelihood Ratio Test (LRT), and Mantel-Haenszel (MH) procedure. Two research interests were investigated: item response theory (IRT) model specification in LC and the LRT and continuity correction in the MH procedure. This study…

This simulation study was conducted to compare the performances of Frequentist and Bayesian approaches in the context of power to detect model misspecification in terms of omitted cross-loading in CFA models with respect to the several variables (number of omitted cross-loading, magnitude of main loading, number of factors, number of indicators…

In Bayesian structural equation modeling (BSEM), prior settings may affect model fit, parameter estimation, and model comparison. This simulation study was to investigate how the priors impact evaluation of relative fit across competing models. The design factors for data generation included sample sizes, factor structures, data distributions, and…

We compared six different analytic models for multitrait-multimethod (MTMM) data in terms of convergence, admissibility, and model fit to 258 samples of previously reported data. Two well-known models, the correlated trait-correlated method (CTCM) and the correlated trait-correlated uniqueness (CTCU) models, were fit for reference purposes in…

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…

Karabatsos compared the power of 36 person-fit statistics using receiver operating characteristics curves and found the "H[superscript T]" statistic to be the most powerful in identifying aberrant examinees. He found three statistics, "C", "MCI", and "U3", to be the next most powerful. These four statistics,…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

Meijer and van Krimpen-Stoop noted that the number of person-fit statistics (PFSs) that have been designed for computerized adaptive tests (CATs) is relatively modest. This article partially addresses that concern by suggesting three new PFSs for CATs. The statistics are based on tests for a change point and can be used to detect an abrupt change…

Item response theory (IRT) has gained an increasing popularity in large-scale educational and psychological testing situations because of its theoretical advantages over classical test theory. Unidimensional graded response models (GRMs) are useful when polytomous response items are designed to measure a unified latent trait. They are limited in…

In single-case research, the multiple baseline design is a widely used approach for evaluating the effects of interventions on individuals. Multiple baseline designs involve repeated measurement of outcomes over time and the controlled introduction of a treatment at different times for different individuals. This article outlines a general…

In this article, we investigate the creation of comparable score scales across countries in international assessments. We examine potential improvements to current score scale calibration procedures used in international large-scale assessments. Our approach seeks to improve fairness in scoring international large-scale assessments, which often…

The current study applied the person-fit statistic, l[subscript z], to data from a Canadian provincial achievement test to explore the usefulness of conducting person-fit analysis on large-scale assessments. Item parameter estimates were compared before and after the misfitting student responses, as identified by l[subscript z], were removed. The…

We compared 5 different statistics (i.e., G index, gamma, "d'", sensitivity, specificity) used in the social sciences and medical diagnosis literatures to assess calibration accuracy in order to examine the relationship among them and to explore whether one statistic provided a best fitting general measure of accuracy. College…

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…

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…