Traditional IRT characteristic curve linking methods ignore parameter estimation errors, which may undermine the accuracy of estimated linking constants. Two new linking methods are proposed that take into account parameter estimation errors. The item- (IWCC) and test-information-weighted characteristic curve (TWCC) methods employ weighting…

While correlated data methods (like random effect models and generalized estimating equations) are commonly applied in practice, students may struggle with understanding the reasons that standard regression techniques fail if applied to correlated outcomes. To this end, this article presents an in-class activity using results from Monte Carlo…

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

Recently, researchers have used multilevel models for estimating intervention effects in single-case experiments that include replications across participants (e.g., multiple baseline designs) or for combining results across multiple single-case studies. Researchers estimating these multilevel models have primarily relied on restricted maximum…

A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the…

The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and…

Likert-type item is the most popular response format for collecting data in social, educational, and psychological studies through scales or questionnaires. However, there is no consensus on whether parametric or non-parametric tests should be preferred when analyzing Likert-type data. This study examined the statistical power of parametric and…

Traditional visualization in meta-analysis uses forest plots to illustrate the combined treatment effect, along with the respective results from primary trials. While the purpose of visualization is clear in the pairwise setting, additional treatments broaden the focus and extend the results to be illustrated in network meta-analysis. The…

Multilevel structural equation (MSEM) models allow researchers to model latent factor structures at multiple levels simultaneously by decomposing within- and between-group variation. Yet the extent to which the sampling ratio (i.e., proportion of cases sampled from each group) influences the results of MSEM models remains unknown. This paper…

Qualitative comparative analysis (QCA) is an influential methodological approach motivated by set theory and boolean logic. QCA proponents have developed algorithms to analyze quantitative data, in a bid to uncover necessary and sufficient conditions where causal relationships are complex, conditional, or asymmetric. This article uses computer…

Large-scale education data are collected via complex sampling designs that incorporate clustering and unequal probability of selection. Multilevel models are often utilized to account for clustering effects. The probability weighted approach (PWA) has been frequently used to deal with the unequal probability of selection. In this study, we examine…

A simulation study was conducted to explore the impact of differential item functioning (DIF) on general factor difference estimation for bifactor, ordinal data. Common analysis misspecifications in which the generated bifactor data with DIF were fitted using models with equality constraints on noninvariant item parameters were compared under data…

We introduce the basics of the Monte Carlo method that allows computing areas and definite integrals, by means of the generation of long sequences of random numbers. The areas of some nontrivial shapes are computed, showing the convergence towards their exact values. The application of the method to the computation of definite integrals is also…

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…