Multidimensional Item Response Theory (MIRT) has been widely used in educational and psychological assessments. It estimates multiple constructs simultaneously and models the correlations among latent constructs. While it provides more accurate results, the unidimensional IRT model is still dominant in real applications. One major reason is that…

Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The…

We develop a "latent variable forest" (LV Forest) algorithm for the estimation of latent variable scores with one or more latent variables. LV Forest estimates unbiased latent variable scores based on "confirmatory factor analysis" (CFA) models with ordinal and/or numerical response variables. Through parametric model…

The cross-classified data structure is ubiquitous in education, psychology, and health outcome sciences. In these areas, assessment instruments that are made up of multiple items are frequently used to measure latent constructs. The presence of both the cross-classified structure and multivariate categorical outcomes leads to the so-called…

Data harmonization is an emerging approach to strategically combining data from multiple independent studies, enabling addressing new research questions that are not answerable by a single contributing study. A fundamental psychometric challenge for data harmonization is to create commensurate measures for the constructs of interest across…

Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and…

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging…

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational…

A recursive equation is proposed for computing higher order derivatives of elementary symmetric functions in the Rasch model. A simulation study indicates a small loss in accuracy for the proposed formula compared to Gustafsson's sum algorithm (1980) for computing higher order derivatives when tests contain 60 items or less. (SLD)