This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate…

An application of Bayesian factor analysis for evaluation of scale reliability is discussed, which is developed within the framework of latent variable modeling. The method permits direct point and interval estimation of the reliability coefficient of multiple-component measuring instruments using Bayesian inference. The approach allows also point…

Educational large-scale assessment (LSA) studies like the program for international student assessment (PISA) provide important information about trends in the performance of educational indicators in cognitive domains. The change in the country means in a cognitive domain like reading between two successive assessments is an example of a trend…

A Bayesian statistics-based approach is discussed that can be used for direct evaluation of the popular Cronbach's coefficient alpha as an internal consistency index for multiple-component measuring instruments, as well as for testing its identity to scale reliability. The method represents an application of confirmatory factor analysis within the…

Questionnaires in educational research assessing students' attitudes and beliefs are low-stakes for the students. As a consequence, students might not always consistently respond to a questionnaire scale but instead provide more random response patterns with no clear link to items' contents. We study inter-individual differences in students'…

It is meaningful to create a comprehensive score to extract information from mass continuous data when they measure the same latent concept. Therefore, this study adopts the logic of psychometrics to conduct scales on continuous data under the Rasch models. This study also explores the effect of different data discretization methods on scale…

The default risk, one of the main risk factors for bonds, should be measured and reflected in the bond yield. Particularly, in the case of financial companies that treat bonds as a major product, failure to properly identify and filter customers' workout status adversely affects returns. This study proposes a two-stage classification algorithm for…

Mixed-format assessments made up of multiple-choice (MC) items and constructed response (CR) items that are scored using rater judgments include unique psychometric considerations. When these item types are combined to estimate examinee achievement, information about the psychometric quality of each component can depend on that of the other. For…

The National Assessment of Educational Progress (NAEP) program only reports state-level subgroup results if it samples at least 62 students identifying with the subgroup. Since some subgroups constitute small proportions of many states' general student populations, these minority subgroups are seldom sufficiently sampled to meet this sample size…

Survey score interpretations are often plagued by sources of construct-irrelevant variation, such as response styles. In this study, we propose the use of an IRTree Model to account for response styles by making use of self-report items and anchoring vignettes. Specifically, we investigate how the IRTree approach with anchoring vignettes compares…

Careful considerations are necessary when there is a need to choose an anchor test form from a list of old test forms for equating under the random groups design. The choice of the anchor form potentially affects the accuracy of equated scores on new test forms. Few guidelines, however, can be found in the literature on choosing the anchor form.…

This software review discusses the capabilities of Stata to conduct item response theory modeling. The commands needed for fitting the popular one-, two-, and three-parameter logistic models are initially discussed. The procedure for testing the discrimination parameter equality in the one-parameter model is then outlined. The commands for fitting…

Measurement error affects the quality of population orderings of an index and, hence, increases the misclassification of the poor and the non-poor groups and affects statistical inferences from binary regression models. Hence, the conclusions about the extent, profile, and distribution of poverty are likely to be misleading. However, the size and…

The purpose of this study is to illustrate the use of functional data analysis (FDA) as a general methodology for analyzing person response functions (PRFs). Applications of FDA to psychometrics have included the estimation of item response functions and latent distributions, as well as differential item functioning. Although FDA has been…

In selected-response assessments such as attitude surveys with Likert-type rating scales, examinees often select from rating scale categories to reflect their locations on a construct. Researchers have observed that some examinees exhibit "response styles," which are systematic patterns of responses in which examinees are more likely to…