In psychology, researchers are often interested in testing hypotheses about mediation, such as testing the presence of a mediation effect of a treatment (e.g., intervention assignment) on an outcome via a mediator. An increasingly popular approach to testing hypotheses is the Bayesian testing approach with Bayes factors (BFs). Despite the growing…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures (DPMs) offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT…

Power analysis based on the analytical t-test is an important aspect of a research study to determine the sample size required to detect the effect for the comparison of two means. The current paper presents a reader-friendly procedure for carrying out the t-test power analysis using the various R add-on packages. While there is a growing of R…

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as…

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student's "t" distributions are used to account for nonnormal…

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…

How can we test whether state-of-the-art generative models, such as Blender and GPT-3, are good AI teachers, capable of replying to a student in an educational dialogue? Designing an AI teacher test is challenging: although evaluation methods are much-needed, there is no off-the-shelf solution to measuring pedagogical ability. This paper reports…

Multilayer perceptron neural networks, Gaussian naive Bayes, and logistic regression classifiers were compared when used to make early predictions regarding one-year college student persistence. Two iterations of each model were built, utilizing a grid search process within 10-fold cross-validation in order to tune model parameters for optimal…

Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing…

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…

E-assessments of students profoundly influence their motivation and play a key role in the educational process. Adapting assessment techniques to current technological advancements allows for effective pedagogical practices, learning processes, and student engagement. The "Handbook of Research on E-Assessment in Higher Education"…

Determining whether individuals belong to different latent classes (taxa) or vary along one or more latent factors (dimensions) has implications for assessment. For example, no instrument can simultaneously maximize the efficiency of categorical and continuous measurement. Methods such as taxometric analysis can test the relative fit of taxonic…

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of…