The Bayesian piecewise growth model (PGM) is a useful class of models for analyzing nonlinear change processes that consist of distinct growth phases. In applications of Bayesian PGMs, it is important to accurately capture growth trajectories and carefully consider knot placements. The presence of missing data is another challenge researchers…

Diagnostic classification models (DCMs) are psychometric models that can be used to estimate the presence or absence of psychological traits, or proficiency on fine-grained skills. Critical to the use of any psychometric model in practice, including DCMs, is an evaluation of model fit. Traditionally, DCMs have been estimated with maximum…

Bayesian approach is becoming increasingly important as it provides many advantages in dealing with complex data. However, there is no well-defined model selection criterion or index in a Bayesian context. To address the challenges, new indices are needed. The goal of this study is to propose new model selection indices and to investigate their…

In relational event networks, the tendency for actors to interact with each other depends greatly on the past interactions between the actors in a social network. Both the volume of past interactions and the time that has elapsed since the past interactions affect the actors' decision-making to interact with other actors in the network. Recently…

The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard good-ness-of-fit statistics. Limited-information fit…

The present study compares the fit of two- and three-parameter logistic (2PL and 3PL) models of item response theory in the performance of preschool children on the Raven's Colored Progressive Matrices. The test of Raven is widely used for evaluating nonverbal intelligence of factor g. Studies comparing models with real data are scarce on the…

Testing item-level fit is important in scale development to guide item revision/deletion. Many item-level fit indices have been proposed in literature, yet none of them were directly applicable to an important family of models, namely, the higher order item response theory (HO-IRT) models. In this study, chi-square-based fit indices (i.e., Yen's…

We present computational modeling results based on a self-paced reading study investigating number attraction effects in Eastern Armenian. We implement three novel computational models of agreement attraction in a Bayesian framework and compare their predictive fit to the data using k-fold cross-validation. We find that our data are better…

Theories of perceptual decision making have been dominated by the idea that evidence accumulates in favor of different alternatives until some fixed threshold amount is reached, which triggers a decision. Recent theories have suggested that these thresholds may not be fixed during each decision but change as time passes. These collapsing…

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior…

Research in education has become increasingly reliant on statistical modeling frameworks to be reflective of the subject matter, to accurately assess what students know and can do, to assist instructors with curriculum design by supplementing informative feedback, and to support policy-makers when making evidence-based decisions. A common feature…

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…