Correct specifications of hierarchical attribute structures in analyses using diagnostic classification models (DCMs) are pivotal because misspecifications can lead to biased parameter estimations and inaccurate classification profiles. This research is aimed to demonstrate DCM analyses with various hierarchical attribute structures via Bayesian…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…

Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in turn, have potentially transformed Bayesian education at the undergraduate level. This article provides an…

We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern Bayesian computing techniques not only for implementing Bayesian methods, but also to deepen students'…

Specialized imputation routines for multilevel data are widely available in software packages, but these methods are generally not equipped to handle a wide range of complexities that are typical of behavioral science data. In particular, existing imputation schemes differ in their ability to handle random slopes, categorical variables,…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian…

Item Response Theory (IRT) is a ubiquitous model for understanding humans based on their responses to questions, used in fields as diverse as education, medicine and psychology. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving test scoring and better informing public policy. Yet larger…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…

Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional "t" tests) when certainty in the estimate is…

The introduction of the intelligence in teaching software is the object of this paper. In software elaboration process, one uses some learning techniques in order to adapt the teaching software to characteristics of student. Generally, one uses the artificial intelligence techniques like reinforcement learning, Bayesian network in order to adapt…

This conference presentation demonstrates a multilevel model for analyzing single case designs. The model is implemented in the Bayesian program WinBUGS. The authors show how it is possible to estimate a d-statistic like the one in Hedges, Pustejovsky and Shadish (2012) in this program. Results are demonstrated on an example.

One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…