For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

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…

Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…

The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study…

Mediation is a causal process that evolves over time. Thus, a study of mediation requires data collected throughout the process. However, most applications of mediation analysis use cross-sectional rather than longitudinal data. Another implicit assumption commonly made in longitudinal designs for mediation analysis is that the same mediation…

Latent class analysis is an analytic technique often used in educational and psychological research to identify meaningful groups of individuals within a larger heterogeneous population based on a set of variables. This technique is flexible, encompassing not only a static set of variables but also longitudinal data in the form of growth mixture…

The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first…

Correlation attenuation due to measurement error and a corresponding correction, the deattenuated correlation, have been known for over a century. Nevertheless, the deattenuated correlation remains underutilized. A few studies in recent years have investigated factors affecting the deattenuated correlation, and a couple of them provide alternative…

Common estimators of interrater reliability include Pearson product-moment correlation coefficients, Spearman rank-order correlations, and the generalizability coefficient. The purpose of this study was to examine the accuracy of estimators of interrater reliability when varying the true reliability, number of scale categories, and number of…

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

We present a new paradigm that allows simplified testing of multiparameter hypotheses in the presence of incomplete data. The proposed technique is a straight-forward procedure that combines the benefits of two powerful data analytic tools: multiple imputation and nested-model ?2 difference testing. A Monte Carlo simulation study was conducted to…

Planned missing data designs allow researchers to increase the amount and quality of data collected in a single study. Unfortunately, the effect of planned missing data designs on power is not straightforward. Under certain conditions using a planned missing design will increase power, whereas in other situations using a planned missing design…

Planned missing designs are becoming increasingly popular, but because there is no consensus on how to implement them in longitudinal research, we simulated longitudinal data to distinguish between strategies of assigning items to forms and of assigning forms to participants across measurement occasions. Using relative efficiency as the criterion,…

The short-term emphasis engendered by No Child Left Behind (NCLB) has focused research predominantly on unraveling the complexities and uncertainties in assessing short-term results, rather than developing methods and assessing results over the longer term. In this paper we focus on estimating long-term gains and address questions important to…