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 simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…

For proper assessment selection understanding the statistical similarities amongst assessments that measure the same, or very similar, topics is imperative. This study seeks to extend the comparative analysis between the brief electricity and magnetism assessment (BEMA) and the conceptual survey of electricity and magnetism (CSEM) presented by…

Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…

Item response theory (IRT) has so many advantages than its precedent Classical Test Theory (CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not…

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

Scientific models and modeling play an important role in science, and students' understanding of scientific models is essential for their understanding of scientific concepts. The measurement instrument of "Students' Understanding of Models in Science" (SUMS), developed by Treagust, Chittleborough & Mamiala ("International…

Cognitive diagnostic models (CDM) have been around for more than a decade but their application is far from widespread for mainly two reasons: (1) CDMs are novel, as compared to traditional IRT models. Consequently, many researchers lack familiarity with them and their properties, and (2) Software programs doing CDMs have been expensive and not…

Cognitive diagnosis models (CDMs) continue to generate interest among researchers and practitioners because they can provide diagnostic information relevant to classroom instruction and student learning. However, its modeling component has outpaced its complementary component-test construction. Thus, most applications of cognitive diagnosis…

Models of modern test theory imply statistical independence among responses, generally referred to as "local independence." One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model,…

In this rejoinder, Maydeu-Olivares states that, in item response theory (IRT) measurement applications, the application of goodness-of-fit (GOF) methods informs researchers of the discrepancy between the model and the data being fitted (the room for improvement). By routinely reporting the GOF of IRT models, together with the substantive results…

Most of the tests and inventories used by counseling psychologists have been developed using CTT; IRT derives from what is called latent trait theory. A number of important differences exist between CTT- versus IRT-based approaches to both test development and evaluation, as well as the process of scoring the response profiles of individual…

In 1997, based on the amendments to Individuals with Disabilities Education Act (IDEA), all states were faced with a statutory requirement to develop and implement alternate assessments for students with disabilities unable to participate in the statewide large-scale assessment. States were given the challenge of creating, implementing, and…

Background: Most instruments that assess quality of life have been validated by means of the classical test theory (CTT). However, CTT limitations have resulted in the development of alternative models, such as the Rasch rating scale model (RSM). The main goal of this paper is testing and improving the psychometric properties of the INTEGRAL…