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…

Among neurotypical adults, errors made with high confidence (i.e. errors a person strongly believed they would not make) are corrected more reliably than errors made with low confidence. This 'hypercorrection effect' is thought to result from enhanced attention to information that reflects a 'metacognitive mismatch' between one's beliefs and…

Bayesian algorithms have been used successfully in the social and behavioral sciences to analyze dichotomous data particularly with complex structural equation models. In this study, we investigate the use of the Polya-Gamma data augmentation method with Gibbs sampling to improve estimation of structural equation models with dichotomous variables.…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes of the same units under different treatment conditions. Because for each unit at most one of the potential…

We have been looking at two different numbers that have been used to describe the availability of physics in U.S. high schools: 60% and 95%. Last month we noted that the U.S. Department of Education Office of Civil Rights (OCR) includes over 7,000 more public schools in the denominator than American Institute of Physics (AIP) Statistics does.…

Although immediacy is one of the necessary criteria to show strong evidence of a causal relation in SCDs, no inferential statistical tool is currently used to demonstrate it. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. Unlike visual analysis that considers only 3-5 observations in…

Meta-analyses in orphan diseases and small populations generally face particular problems, including small numbers of studies, small study sizes and heterogeneity of results. However, the heterogeneity is difficult to estimate if only very few studies are included. Motivated by a systematic review in immunosuppression following liver…

In network meta-analysis, the use of fixed baseline treatment effects (a priori independent) in a contrast-based approach is regularly preferred to the use of random baseline treatment effects (a priori dependent). That is because, often, there is not a need to model baseline treatment effects, which carry the risk of model misspecification.…

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct…

This research focuses on developing and implementing a continuous Naïve Bayesian classifier for GEAR courses at Rio Salado Community College. Previous implementation efforts of a discrete version did not predict as well, 70%, and had deployment issues. This predictive model has higher prediction, over 90%, accuracy for both at-risk and successful…

This article illustrates five different methods for estimating Angoff cut scores using item response theory (IRT) models. These include maximum likelihood (ML), expected a priori (EAP), modal a priori (MAP), and weighted maximum likelihood (WML) estimators, as well as the most commonly used approach based on translating ratings through the test…

Mixture item response theory (IRT) models have been suggested as an efficient method of detecting the different response patterns derived from latent classes when developing a test. In testing situations, multiple latent traits measured by a battery of tests can exhibit a higher-order structure, and mixtures of latent classes may occur on…