Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

Audit studies testing for discrimination have been criticized because applicants from different groups may not appear identical to employers. Correspondence studies address this criticism by using fictitious paper applicants whose qualifications can be made identical across groups. However, Heckman and Siegelman (1993) show that group differences…

Hierarchical Linear Modeling (HLM) sample size recommendations are mostly made with traditional group-design research in mind, as HLM as been used almost exclusively in group-design studies. Single-case research can benefit from utilizing hierarchical linear growth modeling, but sample size recommendations for growth modeling with HLM are scarce…

Theoretical models specifying indirect or mediated effects are common in the social sciences. An indirect effect exists when an independent variable's influence on the dependent variable is mediated through an intervening variable. Classic approaches to assessing such mediational hypotheses (Baron & Kenny, 1986; Sobel, 1982) have in recent years…

In social and business sciences, the importance of the analysis of interaction effects between manifest as well as latent variables steadily increases. Researchers using partial least squares (PLS) to analyze interaction effects between latent variables need an overview of the available approaches as well as their suitability. This article…

The taxometric method effectively distinguishes between dimensional (1-class) and taxonic (2-class) latent structure, but there is virtually no information on how it responds to polytomous (3-class) latent structure. A Monte Carlo analysis showed that the mean comparison curve fit index (CCFI; Ruscio, Haslam, & Ruscio, 2006) obtained with 3…

Most of the statistical procedures in meta-analysis are based on the estimation of average effect sizes from a set of primary studies. The optimal weight for averaging a set of independent effect sizes is the inverse variance of each effect size, but in practice these weights have to be estimated, being affected by sampling error. When assuming a…

The problem with "classical" statistics all invoking the mean is that these estimates are notoriously influenced by atypical scores (outliers), partly because the mean itself is differentially influenced by outliers. In theory, "modern" statistics may generate more replicable characterizations of data, because at least in some…

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach.…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

To realize the benefits of item response theory (IRT), one must have model-data fit. One facet of a model-data fit investigation involves assessing the tenability of the conditional item independence (CII) assumption. In this Monte Carlo study, the comparative performance of 10 indices for identifying conditional item dependence is assessed. The…

In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…

In this article, three multilevel models for meta-analysis are examined. Hedges and Olkin suggested that effect sizes follow a noncentral "t" distribution and proposed several approximate methods. Raudenbush and Bryk further refined this model; however, this procedure is based on a normal approximation. In the current research literature, this…

In "Dusky v. United States" (1960), the U.S. Supreme Court articulated 3 abilities that determine a criminal defendant's competence to stand trial: He or she must be able to consult with counsel, have a factual understanding of the proceedings, and have a rational understanding of the proceedings. Although the legal determination of a defendant's…

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…