A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

Approaches to correcting correlation coefficients for range restriction have been developed under the framework of large sample theory. The accuracy of missing data techniques for correcting correlation coefficients for range restriction has thus far only been investigated with relatively large samples. However, researchers and evaluators are…

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis…

The informativity of a computational model of language acquisition is directly related to how closely it approximates the actual acquisition task, sometimes referred to as the model's "cognitive plausibility." We suggest that though every computational model necessarily idealizes the modeled task, an informative language acquisition…

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…

Our visual brain is remarkable in extracting invariant properties from the noisy environment, guiding selection of where to look and what to identify. However, how the brain achieves this is still poorly understood. Here we explore interactions of local context and global structure in the long-term learning and retrieval of invariant display…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

Purpose: The purpose of this study was to empirically examine the utility of self-determination theory (SDT) within the engagement-performance linkage. Design/methodology/approach: Bayesian multi-measurement mediation modeling was used to estimate the relation between SDT, engagement and a proxy measure of performance (e.g. work intentions) (N =…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix [sigma] of group-level varying coefficients are often degenerate. One can do better, even…

The field of topic modeling has become increasingly important over the past few years. Topic modeling is an unsupervised machine learning way to organize text (or image or DNA, etc.) information such that related pieces of text can be identified. This paper/session will present/discuss the current state of topic modeling, why it is important, and…

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However,…

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

Analyzing the rate at which languages change can clarify whether similarities across languages are solely the result of cognitive biases or might be partially due to descent from a common ancestor. To demonstrate this approach, we use a simple model of language evolution to mathematically determine how long it should take for the distribution over…

Empirical Bayes' (EB) estimation is a widely used procedure to calculate teacher value-added. It is primarily viewed as a way to make imprecise estimates more reliable. In this paper we review the theory of EB estimation and use simulated data to study its ability to properly rank teachers. We compare the performance of EB estimators with that of…