Computer adaptive testing (CAT) is an increasingly common mode of test administration offering improved test security, better measurement precision, and the potential for shorter testing experiences. This article presents a new item selection algorithm based on a generalized objective function to support multiple types of testing conditions and…

Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores,…

The multistage testing (MST) design has been gaining attention and popularity in educational assessments. For testing programs that have small test-taker samples, it is challenging to calibrate new items to replenish the item pool. In the current research, we used the item pools from an operational MST program to illustrate how research studies…

Researchers frequently use Mokken scale analysis (MSA), which is a nonparametric approach to item response theory, when they have relatively small samples of examinees. Researchers have provided some guidance regarding the minimum sample size for applications of MSA under various conditions. However, these studies have not focused on item-level…

This study evaluates various scoring methods including number-correct scoring, IRT theta scoring, and hybrid scoring in terms of scale-score stability over time. A simulation study was conducted to examine the relative performance of five scoring methods in terms of preserving the first two moments of scale scores for a population in a chain of…

The Kaufman Brief Intelligence Test--Second Edition (KBIT-2) is designed to measure verbal and nonverbal abilities in a wide range of individuals from 4 years 0 months to 90 years 11 months of age. This study examines both the advantages of using Mokken Scale Analysis (MSA) in intelligence tests and the hierarchical order of the items in the…

One of the primary goals of international large-scale assessments in education is the comparison of country means in student achievement. This article introduces a framework for discussing differential item functioning (DIF) for such mean comparisons. We compare three different linking methods: concurrent scaling based on full invariance,…

This booklet is a conceptual introduction to item response theory (IRT), which many large-scale testing programs use for constructing and scoring their tests. Although IRT is essentially mathematical, the approach here is nonmathematical, in order to serve as an introduction on the topic for people who want to understand why IRT is used and what…

Vertical scaling is used to put tests of different difficulty onto a common metric. The Rasch model is often used to perform vertical scaling, despite its strict functional form. Few, if any, studies have examined anchor item choice when using the Rasch model to vertically scale data that do not fit the model. The purpose of this study was to…

The need to determine the correct dimensionality of theoretical constructs and generate valid measurement instruments when underlying items are categorical has generated a significant volume of research in the social sciences. This article presents two studies contrasting different categorical exploratory techniques. The first study compares…

In recent years, the interest in measuring growth in student ability in various subjects between different grades in school has increased. Therefore, good precision in the estimated growth is of importance. This paper aims to compare estimation methods and test designs when it comes to precision and bias of the estimated growth of mean ability…

When scaling psychological tests with methods of item response theory it is necessary to investigate to what extent the responses correspond to the model predictions. In addition to the statistical evaluation of item misfit, the question arises as to its practical significance. Although item removal is undesirable for several reasons, its…

The dimensionality is one of the most investigated concepts in the psychological assessment, and there are many ways to determine the dimensionality of a measured construct. The Automated Item Selection Procedure (AISP) and the DETECT are non-parametric methods aiming to determine the factorial structure of a data set. In the current study,…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

Raven's Standard Progressive Matrices (Raven 1941) is a widely used 60-item long measure of general mental ability. It was recently suggested that, for situations where taking this test is too time consuming, a shorter version, comprised of only the last series of the Standard Progressive Matrices (Myszkowski and Storme 2018) could be used, while…