Recent approaches to the detection of cheaters in tests employ detectors from the field of machine learning. Detectors based on supervised learning algorithms achieve high accuracy but require labeled data sets with identified cheaters for training. Labeled data sets are usually not available at an early stage of the assessment period. In this…

Multidimensionality and hierarchical data structure are common in assessment data. These design features, if not accounted for, can threaten the validity of the results and inferences generated from factor analysis, a method frequently employed to assess test dimensionality. In this article, we describe and demonstrate the application of the…

Setting cutoff scores is one of the most common practices when using scales to aid in classification purposes. This process is usually done univariately where each optimal cutoff value is decided sequentially, subscale by subscale. While it is widely known that this process necessarily reduces the probability of "passing" such a test,…

The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels--one for the responses and one for the response times--that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a…

Methods to handle ordered-categorical indicators in latent variable interactions have been developed, yet they have not been widely applied. This article compares the performance of two popular latent variable interaction modeling approaches in handling ordered-categorical indicators: unconstrained product indicator (UPI) and latent moderated…

The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem…

Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph,…

This note highlights and illustrates the links between item response theory and classical test theory in the context of polytomous items. An item response modeling procedure is discussed that can be used for point and interval estimation of the individual true score on any item in a measuring instrument or item set following the popular and widely…

This inquiry is focused on three indicators of the precision of measurement--conditional on fixed values of ?, the latent variable of item response theory (IRT). The indicators that are compared are (1) The traditional, conditional standard errors, s(eX|?) = CSEM; (2) the IRT-based conditional standard errors, s[subscript irt](eX|?)=C[subscript…

Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory…

This article extends the procedure outlined in the article by Raykov, Marcoulides, and Tong for testing congruence of latent constructs to the setting of binary items and clustering effects. In this widely used setting in contemporary educational and psychological research, the method can be used to examine if two or more homogeneous…

Psychometric measurement models are only valid if measurement invariance holds between test takers of different groups. Global model tests, such as the well-established likelihood ratio (LR) test, are sensitive to violations of measurement invariance, such as differential item functioning and differential step functioning. However, these…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

Test tampering, especially on tests for educational accountability, is an unfortunate reality, necessitating that the state (or its testing vendor) perform data forensic analyses, such as erasure analyses, to look for signs of possible malfeasance. Few statistical approaches exist for detecting fraudulent erasures, and those that do largely do not…

When competence tests are administered, subjects frequently omit items. These missing responses pose a threat to correctly estimating the proficiency level. Newer model-based approaches aim to take nonignorable missing data processes into account by incorporating a latent missing propensity into the measurement model. Two assumptions are typically…