This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item…

Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is…

Notwithstanding a large body of literature on log-linear models and odds ratios, no general marginal-free index of the association in a contingency table has gained a wide acceptance. Building on a framework developed by L. A. Goodman, we put into light the direct links between odds ratios, the Altham index, the intrinsic association coefficient,…

We provide tools for identification and exploration of data with very large variability having power law tails. Such data describe extreme features of processes such as fire losses, flood, drought, financial gain/loss, hurricanes, population of cities, among others. Prediction and quantification of extreme events are at the forefront of the…

Contextual, identity, and cultural factors are not only associated with student outcomes but can also serve to moderate the effects of interventions. However, the conventional analysis of moderation commonly used in school psychology is subject to the selection bias potentially introducing bias into estimated moderator effects. This article…

The purpose of this two-part study is to evaluate methods for multiple group analysis when the comparison group is at the within level with multilevel data, using a multilevel factor mixture model (ML FMM) and a multilevel multiple-indicators multiple-causes (ML MIMIC) model. The performance of these methods was evaluated integrally by a series of…

Mediation has played a critical role in developmental theory and research. Yet, developmentalists rarely discuss the methodological challenges of establishing causality in mediation analysis or potential strategies to improve the identification of causal mediation effects. In this article, we discuss the potential outcomes framework from…

Psychology research often focuses on interactions, and this has deep implications for inference from non-representative samples. For the goal of estimating average treatment effects, we propose to fit a model allowing treatment to interact with background variables and then average over the distribution of these variables in the population. This…

The Program for the International Assessment of Adult Competencies (PIAAC) is a multicycle international survey of adult skills and competencies sponsored by the Organization for Economic Cooperation and Development (OECD). The survey examines a range of basic skills in the information age and assesses these adult skills consistently across…

In order to effectively grade persuasive writing we must be able to reliably identify and extract extract argument structures. In order to do this we must classify arguments by their structural roles (e.g., major claim, claim, and premise). Current approaches to classification typically rely on statistical models with heavy feature-engineering or…

Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

Empirical studies often demonstrate multiple causal mechanisms potentially involving simultaneous or causally related mediators. However, researchers often use simple mediation models to understand the processes because they do not or cannot measure other theoretically relevant mediators. In such cases, another potentially relevant but unobserved…

When designing a study for causal mediation analysis, it is crucial to conduct a power analysis to determine the sample size required to detect the causal mediation effects with sufficient power. However, the development of power analysis methods for causal mediation analysis has lagged far behind. To fill the knowledge gap, I proposed a…

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of…

Monte Carlo simulation is a useful tool for researchers to estimated accuracy of a statistical model. It is usually used for investigating parameter estimation procedure or violation of assumption for some given conditions. To run a simulation either the paid software or open source but free program such as R is need to be used. For that,…