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…

Person-fit analyses are commonly used to detect aberrant responding in self-report data. Nonparametric person fit statistics do not require fitting a parametric test theory model and have performed well compared to other person-fit statistics. However, detection of aberrant responding has primarily focused on dominance response data, thus the…

Rater fit analyses provide insight into the degree to which rater judgments correspond to expected properties, as defined within a measurement framework. Parametric models such as the Rasch model provide a useful framework for evaluating rating quality; however, these models are not appropriate for all assessment contexts. The purpose of this…

In order to reach valid and reliable test scores, various test theories have been developed, and one of them is nonparametric item response theory (NIRT). Mokken Models are the most widely known NIRT models which are useful for small samples and short tests. Mokken Package is useful for Mokken Scale Analysis. An important issue about validity is…

A major challenge in the widespread application of Mokken scale analysis (MSA) to educational performance assessments is the requirement of complete data, where every rater rates every student. In this study, simulated and real data are used to demonstrate a method by which researchers and practitioners can apply MSA to incomplete rating designs.…

This study examines and compares four person-fit statistics (PFSs) in the framework of the "D"- scoring method (DSM): (a) van der Flier's "U3" statistic; (b) "Ud" statistic, as a modification of "U3" under the DSM; (c) "Zd" statistic, as a modification of the "Z3 (l[subscript z])"…

The purpose of this study is to describe how Guttman, Rasch, and Mokken approached issues related to invariant measurement. These measurement theorists were chosen to illustrate the evolution of our conceptualizations of invariant measurement during the 20th century within the research tradition of item response theory. Item response theory can be…