As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

Educational and psychological constructs are normally measured by multifaceted dimensions. The measured construct is defined and measured by a set of related subdomains. A bifactor model can accurately describe such data with both the measured construct and the related subdomains. However, a limitation of the bifactor model is the orthogonality…

Most computerized adaptive tests (CAT) have been studied under the framework of unidimensional item response theory. However, many psychological variables are multidimensional and might benefit from using a multidimensional approach to CAT. In addition, a number of psychological variables (e.g., quality of life, depression) can be conceptualized…

In this paper, the efficiency of conditional maximum likelihood (CML) and marginal maximum likelihood (MML) estimation of the item parameters of the Rasch model in incomplete designs is investigated. The use of the concept of F-information (Eggen, 2000) is generalized to incomplete testing designs. The scaled determinant of the F-information…

In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two…