Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has…

Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a…

Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the…

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

Although statistical practices to evaluate intervention effects in SCEDs have gained prominence in the recent times, models are yet to incorporate and investigate all their analytic complexities. Most of these statistical models incorporate slopes and autocorrelations both of which contribute to trend in the data. The question that arises is…

Text is a burgeoning data source for psychological researchers, but little methodological research has focused on adapting popular modeling approaches for text to the context of psychological research. One popular measurement model for text, topic modeling, uses a latent mixture model to represent topics underlying a body of documents. Recently,…

Correct specifications of hierarchical attribute structures in analyses using diagnostic classification models (DCMs) are pivotal because misspecifications can lead to biased parameter estimations and inaccurate classification profiles. This research is aimed to demonstrate DCM analyses with various hierarchical attribute structures via Bayesian…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. (2020) estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores,…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores, including…

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables…

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in…

The present study proposes a Bayesian approach for estimating and testing the operation-specific learning model, a variant of the linear logistic test model that allows for the measurement of the learning that occurs during a test as a result of the repeated use of the operations involved in the items. The advantages of using a Bayesian framework…

This report aims to showcase the value of implementing a Bayesian framework to analyse and report results from international large-scale surveys and provide guidance to users who want to analyse the data using this approach. The motivation for this report stems from the recognition that Bayesian statistical inference is fast becoming a popular…