In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact…

Severity and centrality are two main kinds of rater effects posing threats to the validity and fairness of performance assessments. Adopting Jin and Wang's (2018) extended facets modeling approach, we separately estimated the magnitude of rater severity and centrality effects in the web-based TestDaF (Test of German as a Foreign Language) writing…

This paper studies the use of Reinforcement Learning (RL) policies for optimizing the sequencing of online learning materials to students. Our approach provides an end to end pipeline for automatically deriving and evaluating robust representations of students' interactions and policies for content sequencing in online educational settings. We…

With the continuous development of education, personalized learning has attracted great attention. How to evaluate students' learning effects has become increasingly important. In information technology courses, the traditional academic evaluation focuses on the student's learning outcomes, such as "scores" or "right/wrong,"…

For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…

The random-effects model, applied in most meta-analyses nowadays, typically assumes normality of the distribution of the effect parameters. The purpose of this study was to examine the performance of various random-effects methods (standard method, Hartung's method, profile likelihood method, and bootstrapping) for computing an average effect size…

When testing a statistical mediation model, it is assumed that factorial measurement invariance holds for the mediating construct across levels of the independent variable X. The consequences of failing to address the violations of measurement invariance in mediation models are largely unknown. The purpose of the present study was to…

Previous research includes frequent admonitions regarding the importance of establishing connectivity in data collection designs prior to the application of Rasch models. However, details regarding the influence of characteristics of the linking sets used to establish connections among facets, such as locations on the latent variable, model-data…

Factors that predict political party affiliation are of particular importance in research due to the wider implications in politics and policy making. Extending this line of work, the idea that creativity predicts party affiliation was tested using 2 conceptualizations of creativity: creative personality and creative ideation. Participants (N…

Despite its importance to structural equation modeling, model evaluation remains underdeveloped in the Bayesian SEM framework. Posterior predictive p-values (PPP) and deviance information criteria (DIC) are now available in popular software for Bayesian model evaluation, but they remain under-utilized. This is largely due to the lack of…

Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such…

Determining the number of dimensions underlying many variables in the data or many items in the test is a crucial process prior to performing exploratory factor analysis. Failure to do so leads to serious consequences concerning construct validity. Parallel analysis (PA) has been found to be useful to determine the number of dimensions (i.e.,…

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'…

The present study examines bias in parameter estimates and standard error in cross-classified random effect modeling (CCREM) caused by omitting the random interaction effects of the cross-classified factors, focusing on the effect of a sample size within cells and ratio of a small cell. A Monte Carlo simulation study was conducted to compare the…