The traditional Elo rating system (ERS), widely used as a student model in adaptive learning systems, assumes unidimensionality (i.e., all items measure a single ability or skill), limiting its ability to handle multidimensional data common in educational contexts. In response, several multidimensional extensions of the Elo rating system have been…

Many large-scale assessments model proficiency with a latent regression on contextual variables. Item-response data are used to estimate the parameters of the latent variable model and are used in conjunction with the contextual data to generate plausible values of individuals' proficiency attributes. These models typically incorporate numerous…

Item response theory (IRT) encompasses a broader class of measurement models than is commonly appreciated by practitioners in educational measurement. For measures of vocabulary and its development, we show how psychological theory might in certain instances support unipolar IRT modeling as a superior alternative to the more traditional bipolar…

Item response theory (IRT) models are often compared with respect to predictive performance to determine the dimensionality of rating scale data. However, such model comparisons could be biased toward nested-dimensionality IRT models (e.g., the bifactor model) when comparing those models with non-nested-dimensionality IRT models (e.g., a…

Traditional IRT and IRTree models are not appropriate for analyzing the item that simultaneously consists of multiple-choice (MC) task and constructed-response (CR) task in one item. To address this issue, this study proposed an item response tree model (called as IRTree-MR) to accommodate items that contain different response types at different…

Knowledge tracing (KT) models predict how students will perform on future interactions, given a sequence of prior responses. Modern approaches to KT leverage "deep learning" techniques to produce more accurate predictions, potentially making personalized learning paths more efficacious for learners. Many papers on the topic of KT focus…

Rating scale analysis techniques provide researchers with practical tools for examining the degree to which ordinal rating scales (e.g., Likert-type scales or performance assessment rating scales) function in psychometrically useful ways. When rating scales function as expected, researchers can interpret ratings in the intended direction (i.e.,…

Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory (CTT) models, which traditionally distinguish between true scores and error scores, the responses are clearly linked to latent traits. It is shown that CTT models can be derived as special cases, but the model class is…

This study conducted a comprehensive comparison of Item Response Theory (IRT) linking methods applied to a bifactor model, examining their performance on both multiple choice (MC) and mixed format tests within the common item nonequivalent group design framework. Four distinct multidimensional IRT linking approaches were explored, consisting of…

This paper presents the item and test information functions of the Rank two-parameter logistic models (Rank-2PLM) for items with two (pair) and three (triplet) statements in forced-choice questionnaires. The Rank-2PLM model for pairs is the MUPP-2PLM (Multi-Unidimensional Pairwise Preference) and, for triplets, is the Triplet-2PLM. Fisher's…

Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and…

Background/purpose: This study aimed to reveal the accuracy of estimation of multiple-choice test items parameters following the models of the item-response theory in measurement. Materials/methods: The researchers depended on the measurement accuracy indicators, which express the absolute difference between the estimated and actual values of the…

A research question that is of interest across many disciplines is whether and how relationships in a network are related to the attributes of the nodes of the network. In this dissertation, we propose two joint frameworks for modeling the relationship between the network and attributes. In the joint latent space model in Chapter 2, shared latent…

Dynamic Item Response Models extend the standard Item Response Theory (IRT) to capture temporal dynamics in learner ability. While these models have the potential to allow instructional systems to actively monitor the evolution of learner proficiency in real time, existing dynamic item response models rely on expensive inference algorithms that…